(Recasts to combine Booker and Warner, adds Warner confirmation)

By Patricia Zengerle

WASHINGTON, Sept 3 (Reuters) - Support for the Iran nuclear deal rose in the U.S. Senate on Thursday when two more Democratic senators, Cory Booker and Mark Warner, came out in favor of the agreement.

Both, however, expressed reservations about the pact and said they would support efforts to keep a hard line on Iran.

"While I choose to support the deal, I am not satisfied with it as a final measure and will support efforts to shore up its weaker points," Warner said in a statement, issued shortly after White House spokesman Josh Earnest surprised reporters at his daily press briefing by announcing the Virginia lawmaker's support.

Booker announced his support in a lengthy statement that called the accord between world powers and Tehran "the better of two flawed options."

"Make no mistake, this deal, while falling short of permanently eliminating Iran's pathways to a nuclear weapon, succeeds in either delaying it or giving us the credible ability to detect significant cheating on their part and respond accordingly," Booker said in a statement that also described a variety of reservations about the accord.

Booker and Warner brought to 36 the list of senators supporting the deal. All are President Barack Obama's fellow Democrats or independents who typically vote with them.

Obama won a foreign policy victory on Wednesday when Senator Barbara Mikulski became the 34th senator to back the nuclear deal. Thirty-four votes in the Senate guarantees that Congress cannot override Obama's veto of any resolution of disapproval against the agreement.

Booker, who represents New Jersey, a state with a large Jewish population, had been seen as a Democrat who might vote against the deal, given the Israeli government's strong opposition to it.

New Jersey's senior senator, Robert Menendez, is one of only two Senate Democrats who has announced his opposition to the nuclear agreement.

Deal backers are now trying to muster 41 votes in the Senate, which would let supporters block a disapproval resolution and keep Obama from having to use his veto power. ID:nL1N1180ZN

There are now eight undecided Democrats in the Senate.

(Reporting by Patricia Zengerle; Additional reporting by Richard Cowan, Susan Heavey and Alina Selyukh; Editing by Eric Beech) ((patricia.zengerle@thomsonreuters.com, www.twitter.com/ReutersZengerle ; 001-202-898-8390; Reuters Messaging: patricia.zengerle.reuters.com@reuters.net))

Keywords: IRAN NUCLEAR/CONGRESS