WASHINGTON  The Obama administration released six Guantánamo detainees to other countries on Thursday, including four Chinese Muslims whose cases drew wide attention as the president has struggled to meet his goal of closing the prison by January.

The day’s events were the biggest steps the administration has taken toward that goal. But the moves did not address central questions, including whether political pressure had made the administration back away from meeting the demand of some countries that the United States accept some prisoners for resettlement to gain their cooperation in accepting others.

The Chinese prisoners, from the largely Muslim Uighur region of western China, arrived in Bermuda early in the day and expressed relief at their first taste of freedom in more than seven years.

“Today you have let freedom ring,” one of the Uighur men, Abdul Nasser, said in a statement thanking the Bermudans. In a long legal fight, a federal appeals court had ridiculed as inadequate the government’s evidence against one of the men and the Bush administration had conceded that none of the 17 Uighurs held at Guantánamo were enemy combatants.