The pair held breakfast talks at 10 Downing St. in Blair's final meeting with a foreign official before he steps down as Britain's prime minister on Wednesday.
Schwarzenegger, a conservative who has put major emphasis on the fight against climate change, praised Blair's "great leadership" on the environment.
He said that during a decade in power, the British leader has "proven to the world that you can do both, you can protect the Earth and protect the economy."
Last year, Schwarzenegger signed legislation that imposed the first statewide cap on greenhouse gases. The move put California at odds with the administration of U.S. President George W. Bush, which has resisted global agreements to limit emissions.
Blair said a declaration on climate change agreed by the G-8 group of industrialized nations earlier this month was a major step forward.
"For the first time at the G-8 a few weeks ago we have an agreement on the basic principles for a new global deal on climate change," Blair told reporters.
The agreement calls for a "substantial cut" in the greenhouse gas emissions blamed for global warming, although it does not commit nations to an exact figure.
On Monday, Schwarzenegger held talks in Paris with new French President Nicolas Sarkozy.
Schwarzenegger said after the talks that he admired Sarkozy "tremendously," and believed he would "put a new energy in the relationship between France and other countries, and our state."
Russia and Iran play in tandem to raise oil prices, while the tandem of the United States and Saudi Arabia has a goal to cause oil prices to collapse
In the region and in the worldб America and China seem to have become the major rivals. The Asia-Pacific region seems to have become the main area of this rivalry