Puigdemont was speaking to reporters in Brussels, where he fled after his region's parliament declared independence from Spain. Should he return, he faces arrest on charges of rebellion, sedition and misuse of funds.
"I am willing to meet Mr Rajoy in Brussels or in any other location in the EU, so long as it is not in the Spanish state, for obvious reasons," he said.
The vote was widely seen as a moment of truth on the independence question, a divisive issue for the wealthy northern region, that has rattled a Europe already shaken by Brexit.
With the secessionists maintaining their parliamentary majority, the move to call snap polls appeared to backfire against Rajoy, who had sacked the regional government and dissolved its parliament over the independence declaration.