US president Barack Obama on Tuesday told America he has no hidden agenda with Russia for his second term, after a revealing gaffe.

Obama was caught on tape Monday telling Russian President Dmitry Medvedev he would have more room to negotiate on missile defense after getting through a November election.

Obama’s Republican rivals immediately went on the offensive – accusing him of making secret deals that would affect national security behind America’s back.

Mitt Romney, the leading Republican contender likely to face Obama this fall, told a San Diego audience the open mic gaffe was “an alarming and troubling development.”

“This is no time for our president to be pulling his punches with the American people, and not telling us what he’s intending to do with regards to our missile defense system, with regards to our military might and with regards to our commitment to Israel,” Romney said.

Romney, a former Massachusetts governor, also issued a statement saying Obama “needs to level with the American public about his real agenda.”

Republican presidential candidate Newt Gingrich also questioned Obama’s motives.

“I’m curious, how many other countries has the president promised that he’d have a lot more flexibility the morning he doesn’t have to answer to the American people?” Gingrich said on CNN.

According to Obama, he merely wants to “work with Russia on the deeply divisive issue of a missile defense shield in Europe,” knowing that only by building trust first on that matter can he make gains on another goal of nuclear arms reductions.

“This is not a matter of hiding the ball,” Obama said, well aware of criticism erupting at home. “I’m on record.”

Still, Obama – now in his second open mic faux pax after having insulting Israeli Prime Minister Binyamin Netanyahu alongside French president Nicolas Sarkozy – had not meant for his initial political assessment to be heard.

“This is my last election,” Obama was heard telling outgoing Russian president Medvedev. “After my election, I have more flexibility.”

For Russia, the issues of nuclear weapons reduction and the proposed missile shield are related. Russian fears of new U.S. missiles at its doorstep in Europe have helped to stymie further progress on nuclear arms reductions after a breakthrough agreement two years ago.

Obama said he wants to spend the rest of this year working through technical issues with the Russians, and said it was not surprising that a deal couldn’t be completed quickly – not before 2013.

“I don’t think it’s any surprise that you can’t start that a few months before presidential and congressional elections in the United States, and at a time when they just completed elections in Russia, and they’re in the process of a presidential transition,” Obama told reporters.