Taiwanese President Chen Shui-bian says a top priority for his second term will be improving ties with China.
Chen is regarded with the deepest suspicion in Beijing
In his inaugural speech on Thursday, he called for dialogue to establish stability with the mainland.
But Mr Chen also defended his controversial plan for constitutional changes, and urged Beijing to respect Taiwan's desire for democracy.
China regards the proposals as a moves towards independence and has threatened to counter them with force.
The inauguration went ahead despite a legal challenge against Mr Chen's re-election in March.
The president won the election by less than 0.2% of the vote, fuelling opposition complaints that the election-eve shooting of Mr Chen unfairly influenced the result.
Speaking in heavy rain behind a bullet-proof glass, Mr Chen said he would try to "reconcile the deep divide" caused by the election and "unify the people of Taiwan".
He also defended his plan for change, saying Taiwan's current constitution was outdated.
He called constitutional reforms his "historic responsibility", saying they were necessary to make the government more efficient so that democracy could progress.
But President Chen made clear the new constitution would not address the issue of sovereignty.
Mr Chen won by 0.2% of votes cast
Recount completed but unlikely to affect result
Separate legal challenge could drag on for months
"I am fully aware that consensus has yet to be reached on issues related to national sovereignty, territory and the subject of unification/independence.
"Therefore, let me explicitly propose that these particular issues be excluded from the present constitutional re-engineering project," he said.
Beijing has warned that it will crush any moves towards Taiwanese independence, even at the cost of its own economic prosperity and good relations with the US.
It kept up its attacks on Thursday, saying Mr Chen's policies were the "greatest threat to peace and stability" in the region,
according to the French news agency AFP.
For his part, Mr Chen in his speech said military threats by China only serve to alienate the people of Taiwan.
"Facing the other side's military build-up, we have to reinforce our national defences,"
The US has condemned China's warnings, saying such language has "no place in international civilised discourse".
The White House reiterated America's commitment to the Taiwan Relations' Act, aimed at ensuring that the island can defend itself.
However Washington has also warned Mr Chen against changing the status quo.
Prime Minister Yu Shyi-kun has been reappointed. He and his cabinet were also sworn in on Thursday.
The ceremony was boycotted by the opposition, which held a rally in Taipei to protest against the official election results.