Senators Lindsey Graham, Kelly Ayotte, John McCain and Ted Cruz said at a news conference they wanted to add a measure, which would give Israel an additional $1.5 billion in military aid, to a bill expected later this year to renew US sanctions on Iran.
Arguing that Congress, not the administration, sets spending policy under US law, they objected to a provision in the new agreement preventing Israel from asking for additional funds from Congress after the new Memorandum of Understanding (MOU) begins at the end of fiscal 2018.
"This is a very dramatic moment in the US-Israel relationship between Congress and the state of Israel. Congress is not going to sit on the sidelines," Graham said.
Graham, who oversees the US foreign aid budget, said Friday that Israel made a mistake by signing a new $38 billion security agreement with the Obama administration. Graham has reportedly already voiced his emphatic objections to the aid deal over the last few days.
The four senators also object to Israel's agreement to return any money if Congress tries to send it more than $3.8 billion per year before then.
Graham said he would introduce legislation to overturn a provision in the agreement that phased out a special arrangement that has allowed Israel for decades to use 26.3 percent of the US aid on its own defense industry instead of on US weapons.
US and Israeli officials signed the agreement on Wednesday. The 10-year, $38 billion package is the largest in US history and was reached after nearly 10 months of negotiations that underscored continuing friction between Obama and Prime Minister Netanyahu.
But Netanyahu decided it would be best to forge a new arrangement with Obama, who leaves office in January, rather than hoping for better terms from the next US administration, according to officials on both sides.
The senators insisted that Netanyahu had been forced into signing because Israel's arch-enemy Iran is growing stronger as it obtains billions of dollars unfrozen under a nuclear agreement reached last year.
"Now is not the time to say that we're going to nickel and dime Israel," Graham said.
Republicans, and some of Obama's fellow Democrats, strongly oppose the nuclear pact, with Republican presidential nominee Donald Trump consistently pledging to tear up the agreement if he is sworn into office. They angered the White House in 2015 by inviting Netanyahu to give an address to Congress opposing it.
They have offered several pieces of legislation to overturn or undermine the nuclear deal, and sought to make it an issue in the 2016 US elections.