WASHINGTON — Israel and the Obama administration have agreed to a historically large sum in defense aid to Israel, but several pro-Israel lawmakers are saying the amount is just not enough.

Sen. Lindsey Graham, the chairman of the Senate State and Foreign Operations Appropriations Subcommittee, said on the eve of a State Department ceremony to sign the deal that he hopes to spearhead millions more for Jerusalem.

"While I think the agreement is important and deserving of respect, I have also made it very clear that Congress is not a party to this agreement nor is this agreement binding on future Congresses," Graham, R-S.C., said in a statement Tuesday night.

"Congress has an independent duty to make a decision about the proper level of support for Israel or our other allies. To suggest this MOU will bind future presidents and congresses for the next decade is constitutionally flawed and impractical."

Though the US government has not released details officially, Defense News first reported over the summer that the latest US offer amounts to $3.8 billion annually, which includes hundreds of millions to be spent in Israel on cooperative missile defense and other pre-agreed joint programs.

The agreement is the follow-on to a $30 billion, 10-year memorandum of understanding (MOU) signed in 2007. Members of Congress were not a party to the negotiations, and the deal is not a formal legal document Congress is bound to uphold.

Earlier in the week, the White House was said to be reluctant to sign the deal because US officials were upset Graham would not go along with the agreement to raise Israel's annual package of military aid from $3.1 billion to $3.3 billion starting in 2018.

"The Israeli prime minister told me the administration is refusing to sign the [deal] until I agree to change my appropriation markup back to $3.1 billion," Graham told The Washington Post, which first reported the disagreement. "I said: 'Tell the administration to go F themselves.' "

Graham said Israeli Prime Minister Benjamin Netanyahu was prepared to sign the deal, but that he didn’t ask Graham directly to stop fighting for something better.

Graham on Tuesday said he will seek a $300 million increase in foreign military financing for Israel, citing threats from Iran, Hezbollah, Hamas and radical Islamists in the Sinai Desert.

Graham too faulted the administration's allocation of "only" $500 million for missile defense, starting in 2018, saying Congress has recommended $600 million. 

"Who really expects that in 2018 — given provocative Iranian behavior, improved Iranian missile technology and the chaotic situation in the Middle East — Israel's defense needs will require less investment?" Graham said.

House Foreign Affairs Committee Ranking Member Eliot Engel, D-N.Y., lauded the MOU as "a wonderful agreement," which will provide Israel with a qualitative military edge over the next decade and fund "a well-rounded group of needs that's unprecedented."

"I'm happy for it, I think it's an enormous amount of money, and it shows the strong bond between Israel and the US, and I commend President Obama for it," said Engel, co-chair of the Congressional Israel Allies Caucus. "You can always say there could be more."

Asked to respond to Graham's position, Engel said the deal was sufficient.

"Sen. Graham is a good friend of mine and a good friend of Israel, and he believes that Israel should get a maximum amount," Engel said. "This MOU is a fine amount, and I'm personally satisfied with it."

Defense News spoke with two other Israel stalwarts in the House who were at least open to the idea of Washington sending more aid to Jerusalem.  

Rep. Brad Sherman, a member of Engel's committee, said he supports the MOU, which he called "a nice plan."

"I could see it being stronger and providing for more," given how effectively the Israeli Defense Force contributes to US national security, said Sherman, D-Calif. "The MOU is an executive plan, and Congress is free to appropriate less or more, and it's more likely to appropriate more than less.

"The Israeli government has apparently agreed not to ask for more, but the last time I checked, the Israeli government doesn't control Lindsey Graham or Brad Sherman."

Rep. Trent Franks, R-Ariz., a member of the House Armed Services Committee and co-chair of the Congressional Israel Allies Caucus with Engel, said Tuesday he had not yet seen the deal, but "completely" agrees with Graham that it "shouldn't be the ceiling, it should be the floor."

"It is impossible to overstate the national security asset Israel is to America," he said.

Franks, who is also co-chair of the bipartisan Missile Defense Caucus, said he had successfully argued for plus-ups to the US funding of cooperative missile defense programs with Israel — such as Iron Dome. Franks, too, favored the $600 billion figure.

The Obama administration "always wants to put pressure on lowering their own budget threshold on missile defense, and certainly that's true with Israel. We've always ignored them and plussed it back up, thank God," Franks said.

Sherman said he would wait until he saw the MOU itself before judging whether it treats missile defense adequately, though he said he could see himself arguing for more for missile defense and for more joint investment in tunnel detection technology.

Sherman alluded to the vast network of advanced tunnels Hezbollah has reportedly built along the border with Israel, and those authorities in the US have found along the US-Mexican border.

"They have a tunnel problem and we have a tunnel problem," he said.

As a condition of expanding Israel's top line from $30 billion to $38 billion over the coming 10 years, Washington is insisting on removing a 30-year-old privilege whereby Israel is able to convert a significant portion of grant dollars into shekels for local research, development and procurement.

Graham condemned the provision, arguing it could cost the US military access to the sort of cutting-edge Israeli technology that as saved the lives of US troops.

"I do not believe this new provision will serve the interests of the United States or Israel," Graham said. "I do fear it will be Americans wearing the uniform of our nation who will pay the price for this short-sighted change in policy."

Aaron Mehta in Washington and Barbara Opall-Rome in Israel contributed to this report.