TAMPA, Florida (Reuters) - President Barack Obama on Thursday urged Israel and the Palestinians to make compromises to help revive peace talks, signaling he has not given up Middle East diplomacy despite his administration’s shaky efforts so far.

Speaking at a townhall-style meeting in Florida, Obama said he was still working to bring the two sides to the negotiating table to resume a peace process that has been frozen for the past 13 months.

He also reasserted his administration’s ability to act as an even-handed broker, saying he was committed to Israel’s security but also was sympathetic to the Palestinians’ plight.

“We are working to try to strengthen the ability of both parties to sit down across the table and to begin serious negotiations,” Obama said.

His efforts to restart talks have made little progress since he took office a year ago with a commitment to make ending the 62-year-old conflict a high priority. Critics say he was naive about obstacles such as Israeli settlement building.

Obama blamed internal politics both in Israel and the Palestinian territories for constraining peace diplomacy.

He cited problems faced by Israeli Prime Minister Benjamin Netanyahu, who the president said “is making some effort to move a little bit further than his coalition wants to go.”

Netanyahu’s right-leaning government includes pro-settler parties strongly opposed to ceding occupied land to the Palestinians for a future state.

Obama said Palestinian President Mahmoud Abbas wants peace but has to contend with Hamas, an Islamist group that denies Israel’s right to exist. Abbas, a pro-U.S. moderate, is also weakened by Hamas’s control of the Gaza Strip.

“Both sides are going to have to make compromises,” Obama said, calling on Israelis to acknowledge Palestinians’ “legitimate grievances” and for the Palestinians to “unequivocally renounce violence” against the Jewish state.

Obama declined, under questioning from an audience member, to condemn Israel for its treatment of Palestinians. “Israel is one of our strongest allies,” he said. “I will never waver from ensuring Israel’s security.”

But he insisted, “The plight of the Palestinians is something that we have to pay attention to. It is not good for our security and for Israel’s security if you have millions of individuals who feel hopeless.”

Many in the Muslim world accused Obama’s predecessor, George W. Bush, of bias in favor of Israel. Obama had pledged full engagement in Middle East peace efforts, something the Bush administration was widely seen as avoiding.

Despite that, Obama made no mention of the Middle East conflict in his State of the Union speech on Wednesday.