Speaking after talks at his family retreat in Kennebunkport, Maine, Mr Bush said he and Mr Putin recognised the need to "send a common message".
The US has accused Iran of seeking nuclear arms, which Iran denies.
But the two leaders failed to resolve differences over the planned US anti-missile defence shield.
Russia has strongly opposed US plans to base parts of the proposed shield near Russia's borders, and recently warned it might target its missiles towards Europe again.
Moscow has also baulked at US-led drives at the UN to impose tougher sanctions against Iran for pursuing its uranium enrichment programme.
Talking to reporters after what officials had billed as a casual meeting, the two leaders projected a united front towards dealing with Iran.
"We're close on recognising that we got to work together to send a common message," said Mr Bush.
Mr Putin said he and Mr Bush would "continue to be successful" in tackling the issue of Iran's nuclear programme through the UN.
On the vexed question of US plans for a missile defence system in Eastern Europe, President Putin brought a range of new proposals.
These included modernising a radar station in Azerbaijan, which he had previously suggested as an alternative site to Poland and the Czech Republic, and including in the programme a new radar facility being built in southern Russia.
"The relationship of our two countries would be raised to an entirely new level," said Mr Putin, standing alongside his host.
He also suggested widening discussions on missile defence to include other European countries and conducting them within the framework of the Russia-Nato council.
The BBC's James Coomarasamy in Kennebunkport says President Putin seems to be moving further away from opposing the US missile defence plans and further towards trying to modify and become involved in them.
President Bush described Mr Putin's proposals as innovative and strategic, but he stressed that Poland and the Czech Republic were an integral part of the missile defence system.
Asked whether he trusted President Putin, the US leader said the Russian president sometimes said things he did not like but that he believed he was honest.