China and Taiwan last spoke formally in 1999, before former Taiwan President Lee Teng-hui enraged Beijing by describing ties as "a special state-to-state relationship".
China has claimed sovereignty over Taiwan since 1949, when Mao Zedong's Communists won the Chinese civil war and Chiang Kai-shek's Nationalists (KMT) fled to the island. Beijing has vowed to bring Taiwan under its rule, by force if necessary.
Yet China, keen to avoid diplomatic rows in the run-up to the Beijing Olympics in August, is expected to take a conciliatory line this week.
Ties have also warmed considerably after the KMT's China-friendly Ma Ying-jeou won the presidency in March.
In a further sign of a thaw, Taiwan's central bank said on Wednesday it would allow financial institutions to sell Chinese yuan to individuals as well as buying the currency from them.
Taiwan's parliament on Thursday approved an amended bill that will help speed the process of allowing wider convertibility between the Taiwan dollar and the yuan signalling improving ties on both sides.
The parliament's approval will let the island's Financial Supervisory Commission and central bank work on plans to let financial institutions buy and sell the Chinese yuan to individuals, which might happen by end-June at the earliest.
But Taiwan's the main opposition Democratic Progressive Party accused the government of courting Beijing because of the ruling party's business connections in China and implored it to "negotiate on equal footing".
"We can't belittle Taiwan's sovereignty, and we can't lose the country's dignity," a party official said in a statement.
There are currently no direct flights between the two rivals except on major holidays, meaning the hundreds of thousands of Taiwanese who live and work in China have to make time-consuming flights via Hong Kong, Macau or other third territories.
"I think it's a good sign," said Beijing university student Jane Chen of the talks. "They can help understanding, and solve problems."
A Taipei resident expressed guarded optimism.
"It's a good start," said Tien Ya-wen, 21, a university law student. "I think it's hard to say that they can sign an agreement due to the differences in the two sides."
