Western nations say Iran is developing a nuclear weapon but Tehran says its programme is for generating electricity.
The chancellor will wait for the European Union to finish its talks with Iran and a report from the International Atomic Energy Agency (IAEA), the UN atomic body, before deciding on any sanctions, she said.
"If the reports remain unsatisfactory... we need to think about further possible sanctions... we also have to then talk and agree on further possible sanctions," she said.
Russia and China, both permanent members of the UN security council, are preventing the UN from imposing a third set of sanctions against Iran.
Bush said that partnership between countries was the key to making progress on Iran's nuclear projects.
"What the Iranian regime must understand is that we will continue to work together to solve this problem diplomatically, which means [Tehran] will continue to be isolated," Bush said on Saturday.
The two leaders also discussed climate change during their talks, with the German chancellor outlining a different strategy on combating climate change than Bush, who believes that greenhouse gas emission reductions should be voluntary.
"This is a very crucial time to really set the agenda for a post-Kyoto regime," she said, referring to upcoming talks to find a new treaty to replace one that currently governs the emissions of signatory nations.
Bush voiced some support for General Pervez Musharraf, Pakistan's president, who imposed a state of emergency last week.
Bush said plans by Musharraf's government to lift a state of emergency within a month and hold parliamentary elections by 15 February were "positive steps".
Other issues such as security in Afghanistan and a planned conference on Middle East peace which is due to be hosted by Bush in a few weeks were discussed.
Merkel's visit also sought to further mend relations between the US and Germany, which soured amid differences over the Iraq war in 2003.
The visit follows meetings that Bush held this week with Nicolas Sarkozy, France's president, in Washington and Virginia, in which both leaders agreed a "common approach" on Iran.