The White House says Mr. Bush encouraged Hu to engage in "substantive dialogue with the Dalai Lama's representatives and to allow access for journalists and diplomats."
Beijing's crackdown in Tibet is in response to the most sustained uprising against Chinese rule in almost two decades, a challenge that has put China's human rights record in the international spotlight.
Mr. Bush also told Hu that last weekend's elections in Taiwan provided "a fresh opportunity for both sides to reach out and engage one another in peacefully resolving their differences."
They also discussed the situation in North Korea and Myanmar.
China on Wednesday announced the surrender of hundreds of people over anti-government protests among Tibetans and allowed into the regional capital Lhasa the first group of foreign journalists to visit since the violence.
The moves appear calculated to bolster government claims that authorities are in control of the situation and that the protests that began peacefully were acts of destruction and murder.
The protests embarrassed the government ahead of this summer's Beijing Olympics, leading it to flood Tibet with troops and ban foreign journalists. The protests took a violent turn on March 14, when rioters set hundreds of fires in Lhasa and attacked ethnic Chinese.
It was unclear how much freedom to report the small group of foreign journalists, among them an Associated Press reporter, would have during the Chinese government-arranged two-day trip. The visit comes amid rising international pressure over China's crackdown in Tibet less than five months ahead of the Beijing Olympics.
State-run media announced that more than 600 people had turned themselves in to police in Lhasa and in Sichuan province, where unrest also broke out.
Police also had published a list of 53 people wanted in connection with the riots, the official Xinhua News Agency reported. At least 29 people have been formally arrested, but it wasn't clear if they were among the 53 on the wanted list.
The uprising was the broadest and most sustained against Chinese rule in almost two decades, embarrassing and frustrating the communist leadership. Thousands of troops and police have been deployed to contain the unrest.
The government says at least 22 people have died in Lhasa; Tibetan rights groups say nearly 140 Tibetans were killed, including 19 in Gansu province.
So far, the U.S., Britain and Germany have all condemned China for its response to the protests, but stopped short of threatening to boycott the games or the Aug. 8 opening ceremony.
The Bush administration, meanwhile, has staked out a position which de-links China's human rights actions from the Olympics, reports CBS News State Department correspondent Charles Wolfson.
"Our view…is that the Olympics is an important international sporting event," said State department spokesman Sean McCormack, adding "On the other side of that, we would encourage the Chinese government to put their best face forward during the Olympics. The world is going to be watching."
But French President Nicolas Sarkozy hasthe opening ceremony.
"Our Chinese friends must understand the worldwide concern that there is about the question of Tibet, and I will adapt my response to the evolutions in the situation that will come, I hope, as rapidly as possible," he told reporters in southwest France.
Belgian Vice Premier Didier Reynders, meanwhile, said officials in his government had not excluded the possibility of staying away from the Games. The sports minister of the northern Dutch-speaking region of Flanders has already said he will not attend the opening ceremony of the games, arguing the ceremony is used to promote Chinese propaganda.
Also Tuesday, China's Foreign Ministry lashed out at a British newspaper editorial comparing the Beijing Olympics to the 1936 Games in Nazi Germany as an "insult to the Chinese people."
The editorial by ex-British Cabinet minister Michael Portillo published in The Sunday Times revealed the "despicable psychology of some people," spokesman Qin Gang said in a statement.
Authorities had pledged harsh punishment for those participating in the violence. The Tibet Daily quoted the national police chief as saying monks would be subjected to "patriotic education" classes and he accused the protesters of violating Buddhist tenants.
In such classes, monks are forced to denounce their spiritual leader, the Dalai Lama, who remains widely revered despite Beijing's relentless vilification, and declare their loyalty to the communist government.
China's communist troops entered Tibet in 1950, and the country claims to have the Himalayan region for seven centuries. Many Tibetans say they were effectively an independent nation for most of that time.