While George Bush urged Hu Jintao, his Chinese counterpart, to support the US efforts to halt the nuclear programmes of North Korea and Iran, the Chinese leader counselled flexibility and diplomacy.
After receiving Hu at the Oval Office, President Bush, said: "We've got a mutual interest in seeing that the Korean Peninsula is nuclear weapons-free."
The last six-party talks on North Korea - involving North Korea, South Korea, the United States, China, Japan and Russia - had ended without progress in November. China is North Korea's main benefactor and key ally.
Hu said China was seeking reconciliation and a peaceful solution to the issue. "The six-party talks have run into some difficulties at the moment. I hope that the parties will be able to further display flexibility, work together and create necessary conditions for the early resumption of the talks."
Bush said that the United States and China had a common goal of ensuring that Iran did not have a nuclear weapon or the capacity to build one.
Earlier, at a White House arrival ceremony, Hu said China would work with the United States and others on both Iran and North Korea. He said China wanted to resolve the issues "through diplomatic negotiation, to uphold the international non-proliferation regime and safeguard peace and stability."
"We are ready to continue to work with the US side and other parties concerned to peacefully resolve the nuclear issue on the Korean Peninsula and the Iranian nuclear issue through diplomatic negotiation"
Hu Jintao, Chinese president
"Both China and the United States are countries of significant influence in the world. We share important common, strategic interests in a wide range of areas, including economic cooperation and trade, security, public health, energy and environmental protection, and on major international and regional issues," Hu said.
"We are ready to continue to work with the US and other parties concerned to peacefully resolve the nuclear issue on the Korean Peninsula and the Iranian nuclear issue through diplomatic negotiation, to uphold the international non-proliferation regime and to safeguard global peace and stability."
The Bush administration has declined to rule out military action, but said it prefers diplomacy in both disputes.
China, a veto-holding member of the UN Security Council, has been reluctant to support punitive action against Iran such as imposing sanctions.
Iran's nuclear programme was
high on the bilateral agenda
Bush said one of the tactics he discussed with Hu was adopting a UN Security Council resolution under a provision of the UN charter, known as Chapter 7, that would make demands such as suspending uranium enrichment legally binding on Iran.
Such a resolution would send "a common message to the Iranians that China and the United States and EU3 (European) countries all deeply are concerned about the Iranian ambition," Bush said.
Britain, France and Germany are the so-called EU3 that have been negotiating with Iran on its nuclear program.
As a first step after the UN's International Atomic Energy Agency report next week on Iran's nuclear activities, the United States, Britain and France hope for a Chapter 7 resolution putting demands on Iran.
But Condoleezza Rice, the US Secretary of State, suggested that the resolution also include targeted sanctions such as a freeze on individual's assets abroad or a travel ban, although Russia and China were considered unlikely to agree.
"China is an important voice in international affairs. And I will continue to work with the president to strategize as to how best to achieve our important goal, which is ... an Iran without the capacity, the know-how, or a nuclear weapon," Bush said.
Hu also made sure to mention another thorny issue between the two countries, that of Taiwan, and China's one nation policy: "President Bush, you and the US government have stated on various occasions that you are committed to the one-China policy, abide by the three Sino-US joint communiques, and oppose Taiwan independence. We appreciate your commitments."
"Taiwan is an inalienable part of Chinese territory. We will continue to make every effort and endeavor with every sincerity to strive for the prospect of peaceful reunification of the two sides across the Taiwan Straits," he said.