The war remains deeply unpopular among Americans, keeping Bush's approval ratings stuck around 30 percent and below.
But a fall in violence has taken much of the steam out of efforts by Democratic congressional leaders to try to link war funding to troop withdrawal timetables, something Bush refuses to accept. Most Democrats maintain, however, that dramatic changes are needed in Bush's Iraq strategy.
TROOP REDUCTIONS
Petraeus is due to report to the U.S. Congress in March on whether more troop reductions are advisable. Asked on Saturday whether more troops could be withdrawn this year, Petraeus said it was possible but no decision had been made.
Despite heavy U.S. pressure, Iraq's main Shi'ite, Sunni Arab and Kurdish political blocs have failed to agree on major laws seen by Washington as crucial to bridging the sectarian divide. Bush conceded the Iraqi government had to do more.
"Have they done enough? No," he said.
Bush earlier made his first presidential visit to Israel and the occupied West Bank, predicting a peace treaty within a year but with no major breakthroughs. Bahrain was the second of five Arab states Bush will visit to enlist their help in containing Iran's growing regional clout.
U.S. Secretary of State Condoleezza Rice said talks would now turn to "the threats that we've seen in the Gulf, the problem of extremism, whether it be extremism from al Qaeda, Sunni extremism, or whether it be Iran and its tentacles, like Hezbollah and the part of Hamas that Iran supports".
Gulf states have battled al Qaeda militants in recent years, but they are also concerned about the crises in Lebanon and Iraq, as well as the standoff over Iran's nuclear programme.
Local media said Kuwait's emir would tell Bush of his concerns that a U.S. strike on nearby Iran would destabilise the Gulf, key to world oil supplies. Bush is likely to hear a similar message from other Gulf Arab leaders fearful of war.
Bush said in Kuwait that Iran and Syria had to stop promoting violence in Iraq.
"Syria needs to further reduce the flow of terrorists to the territory, especially suicide bombers. Iran must stop supporting the militia special groups that attack Iraqi and coalition forces and kidnap and kill Iraqi officials," he said.
