Bush also said he is not looking to set up permanent US military bases in Iraq, although he said he wanted to conclude a deal with Baghdad to keep US forces in the country beyond the year's end.
Senior government officials in Baghdad are opposing the deal, known as a Status of Forces Agreement (Sofa), and say they doubt it can be finalised by the end of July.
A majority of the Iraqi parliament wrote to the US congress last week rejecting the deal with Washington if it is not linked to a requirement for US forces to leave.
Iraqi media has reported the US is seeking to keep as many as 50 military bases in Iraq indefinitely, control the nation's air space, and grant troops and foreign private contractors continuing immunity from prosecution under Iraqi law.
Bush also referred to Iran after his talks with Merkel, saying "all options are on the table" in dealing with Tehran’s uranium enrichment programme.
"I told the chancellor my first choice, of course, is to solve this diplomatically," he said.
Merkel said that additional sanctions would be needed if Tehran does not agree to suspend sensitive nuclear work.
"The offer has been put on the table to Iran, but ... if Iran does not meet its commitments, then further sanctions will simply have to follow," she said.
"We again said we want to give room for diplomatic solutions, we want to give diplomacy a chance, but we also have to stay on that particular issue."
The US and several European nations allege Tehran is looking to produce uranium for a nuclear weapon, despite a consensus National Intelligence Estimate (NIE) of all 16 US spy agencies saying it was believed Iran stopped its nuclear arms work four years ago.
Iran says its enrichment project is solely to generate electricity.
The diplomatic pressure came as Mahmoud Ahmadinejad, Iran's president, said Bush's era "has come to an end".
"If the enemy thinks they can break the Iranian nation with pressure, they are wrong," he said on Wednesday.
Bush is currently on a "farewell tour" of Europe ahead of the end of his term of office in January.