During a meeting at the White House, the two leaders affirmed their common view that Iran must not be allowed to develop nuclear weapons and that it is important the world maintains a united front in confronting Tehran.
'We are in agreement - also - that a diplomatic solution needs to be found,' Merkel said through a translator, adding that 'we do see good chances for bringing this about.'
The meeting came as Britain, France and the United States, with German support, proposed a resolution at the UN Security Council demanding Iran come clean about its nuclear activities and halt uranium enrichment.
'It's very important that the international community send a clear message to the Iranians that a nuclear weapon is unacceptable,' Bush said.
China and Russia have expressed reservations about the resolution under the UN charter's Chapter 7, which would allow the council to impose penalties such as sanctions or even military force if Iran does not comply.
Bush said the United States will work with its allies in negotiating the wording of the resolution, and that the partnership with Europe aimed at curtailing Iran's nuclear ambitions 'won't fold.'
Iran insists that its nuclear programme is purely for generating energy. The United States believes it is being used to secretly develop nuclear weapons.
Merkel has previously urged the United States to hold direct discussions with Iran, but did not say whether the pressed Bush to do so.
Merkel was making her second trip to Washington since taking office in November as the United States and Germany seek to develop a strategy toward Iran.
The US and the European Union have worked to send a strong message to Iran that it must cooperate with international demands to disclose its nuclear work, but have faced resistance on the Security Council from veto-wielding powers China and Russia.
While supporting the effort to prevent Iran from developing nuclear weapons, Merkel opposes the use of military force - which Bush has not ruled out.
'In a situation just as the one that we have now, it is crucial if one wants to see this matter through to a diplomatic success, to actually do this on a step-by-step basis,' Merkel said.
Merkel has sought to strengthen trans-Atlantic ties following the fallout in US-German relations over former chancellor Gerhard Schroeder's opposition to the US-led invasion of Iraq.
The White House largely considers the differences over the conflict as an issue of the past, and, unlike the first meeting between Bush and Merkel in January, sees this one as an opportunity to work on important issues rather than for the two leaders to become acquainted.
'I appreciate Chancellor Merkel's straightforward judgment,' Bush said. 'And I hope that I have created the condition where she tells me what's on her mind and she expresses her beliefs.'
The White House also praised Merkel for taking a strong stance on Iran and working diplomatically to find a solution to the crisis.
Bush and Merkel planned to have a working dinner after their brief appearance before reporters. Other topics on the agenda are Hamas' leadership of the Palestinian authority, the conflict in Sudan's Darfur region and US efforts to get NATO to support peacekeeping there.
During her visit, Merkel was to meet business leaders in New York and address the American Jewish Committee along with Bush on Thursday to mark the organization's 100th anniversary.
Bush said he accepted Merkel's invitation to visit Germany on his way to the G-8 summit July 15-17 in Saint Petersburg, Russia.