Hu made the conciliatory comments in an hour-long talk with Obama that also covered the Iran nuclear dispute and China's demands over Tibet and Taiwan, two areas that recently flared as sore-spots in U.S.-China relations.
The top-level talk capped a week of easing tensions between the two big powers.
China said on Thursday that Hu would attend a summit in Washington on nuclear security later this month and diplomats said Beijing had agreed to join in talks with Western powers about a fresh round of U.N. sanctions against Iran.
"President Obama underscored the importance of working together to ensure that Iran lives up to its international obligations," the White House said in a statement after the telephone call, on Thursday Washington time, which was Friday in Beijing.
"He also emphasized the importance of the United States and China along with other major economies implementing the G20 commitments designed to produce balanced and sustainable growth."
Chinese media reports of the conversation did not mention Iran, instead touching on Hu's desire for talks to resolve trade spats, the importance of healthy ties between the two nations, and stressing Beijing's sensitivity about Tibet and Taiwan.
"Both China and the United States face the task of boosting the economic recovery and maintaining stable economic development," Chinese state television quoted Hu saying.
"I hope that the two sides can well address economic and trade problems via equal consultations and contribute to the broader goal of China and U.S. trade and economic cooperation."
The potentially touchy issue of China's currency, the yuan, did not appear in either country's public account of the chat. But those accounts may not have covered all of their discussion.
The nuclear summit will open days before the U.S. Treasury is due to release a report on whether China is distorting its currency exchange rate to boost its exports.
Domestic U.S. political pressure has been building on the Obama administration to label China a "currency manipulator".
But if it does the slap would come just as ties are improving, and at a time when Washington is seeking help on diplomatic issues such its drive for new sanctions on Iran.
IMPORTANT RELATIONSHIP
The relationship between Beijing and Washington has been dragged down in recent months by disputes spanning China's currency and internet controls, U.S. arms sales to the self-ruled island of Taiwan, and Obama's meeting with exiled Tibetan spiritual leader the Dalai Lama.
Beijing says Taiwan is an illegitimate breakaway from mainland rule, and it condemns the Dalai Lama as a "separatist" for seeking self-rule for his homeland.
Hu stressed that these are still vital concerns for China.
"The Taiwan and Tibet issues are key to China's sovereignty and territorial integrity, and relate to China's core interests. Appropriately handling these issues is key to ensuring the healthy and stable development of U.S.-China ties," he was quoted saying.
"Since President Obama took office, with the hard work of both sides, China-U.S. ties have show a trend of positive development," Hu said.
Both leaders agreed to work hard to ensure positive results at a second round of their Strategic and Economic Dialogue, which will be held in May, Chinese state media reported.
The United States welcomed Hu's decision to attend the nuclear security summit, saying it would allow them to address a "shared interest in stopping nuclear proliferation and protecting against nuclear terrorism".
"They also discussed the importance of developing a positive bilateral relationship," the White House statement added. (Additional reporting by Yu Le, Wang Lan and Zhou Xin in BEIJING, writing by Emma Graham-Harrison; Editing by Sanjeev Miglani)
