BEIJING — Taiwan and China agreed yesterday to set up permanent offices in each other’s territory for the first time in nearly six decades of hostility, one of the biggest trust-building steps they’ve taken in their political rivalry.

There were few details and no time frame was given for establishing the offices, which could perform consular functions such as issuing travel documents.

Yet coming on the first day of formal talks between the sides in a decade, the agreement lends strong momentum toward efforts to build confidence and spur cooperation between the two sides, which divided amid civil war in 1949 and whose relationship has veered between strained to outright hostile.

Foundation Deputy Secretary-General Pong Jian-kuo said a consensus on exchanging offices was reached during morning talks, saying they would “facilitate people’s exchanges and traveling across the Strait.”

The unexpected announcement injected a touch of drama into an otherwise modest agenda that sought mainly to finalize agreements on charter flights and tourism.

“It’s a very positive and healthy development in relations across the Taiwan Strait,” a political scientist of Taiwan’s Chinese Culture University, George Tsai, said.

Also yesterday, China denied accusations by two American lawmakers that it hacked into congressional computers, saying that as a developing country it wasn’t capable of sophisticated cybercrime.

“Is there any evidence? … Do we have such advanced technology? Even I don’t believe it,” a Foreign Ministry spokesman, Qin Gang, told a regularly scheduled news conference.