Chen's invitation on Tuesday followed a historic trip to the mainland by Taiwan's opposition leader Lien Chan that netted a friendship offer of two giant pandas from Beijing.
Chen, visiting Taiwan's small Pacific ally of Kiribati, said he hoped Chinese President Hu Jintao could visit Taiwan to gauge the will of the people.
The invitation appeared to be an attempt at conciliation, although Chen remained steadfast in his pro-independence stance.
"I hope he can come to see for himself whether Taiwan is a sovereign, independent country, and what our 23 million people have in mind," Chen said.
Beijing quickly responded by saying that it will not talk to Chen until his party drops what China says is an independence clause in the party's platform.
Wang Zaixi, a spokesman for the ruling Communist Party's Taiwan Work Office, said Chen's government had also to first endorse a tacit agreement, made between the two sides in 1992, that the self-ruled island and the mainland are "one China".
Lien (L) is the first Kuomintang
leader to visit China in 56 years
He added that Beijing was also willing to discuss its missile deployment with Taiwan if the island acknowledged it was part of China and abandoned its pro-independence stance.
"I think so long both sides sit down and talk on the basis of 'One China', any topic can be put on the table, including the missile issue," Wang said.
Beijing is also to lift restrictions on Chinese tourists travelling to Taiwan.
China has also offered to scrap tariffs on more than 10 kinds of fruits from Taiwan and allow imports of six more fruit types, bringing the total to 18, Xinhua news agency said on Tuesday.
Before leaving Shanghai for Taipei on Tuesday, opposition leader Lien said the gestures from Beijing were good for cross-strait ties, Xinhua reported.
The decision to scrap fruit tariffs and allow more varieties into the mainland "is of great significance to farmers in the central and southern parts of Taiwan. The KMT (Kuomintang or Nationalist Party) will actively facilitate the issue once we're back in Taiwan," Lien said.
Lien is the first chairman of the KMT to set foot on mainland China since 1949 when the Communists swept to power and the KMT fled to Taiwan.
"I hope he can come to see for himself whether Taiwan is a sovereign, independent country, and what our 23 million people have in mind"
President Chen Shui-bian
But the fate of what Xinhua called "clear gestures of affinity" towards Taiwan is in the hands of the island's government under president Chen.
There are currently many restrictions on mainland Chinese going to Taiwan - not just from the Chinese side.
Ordinary citizens cannot go as tourists to the island as they need invitations from Taiwan groups, such as professional delegations or academic institutions.
"Tourism administration and all relevant parties on the mainland welcome organisations from Taiwan's tourism industry to start consultations with us on an earlier date in order to make detailed arrangements accordingly," Xinhua quoted Chen Yunlin, Minister of China's Taiwan Affairs Office, as saying.
China said Taiwanese made 3.7 million trips to the mainland in 2004, while only 145,000 mainlanders visited Taiwan.