Torra made a request to meet Rajoy earlier in the day from Berlin, where he was visiting deposed Catalan leader Carles Puigdemont as controversy grows over his appointment, with critics accusing him of "xenophobia" for past comments deemed offensive to the Spanish.
"My first aim of this new Catalan government is to offer dialogue to the Spanish government," he told reporters.
Prime Minister "Rajoy please you fix a time and place," he said, standing next to Puigdemont, who is battling extradition to Spain on charges of rebellion and misuse of public funds.
Rajoy responded from Sofia where he held talks with his Bulgarian counterpart that he would meet him, although he cautioned that Torra would have to respect the law and added there would never be an independent Catalan republic.
Torra, who was handpicked by Puigdemont as his successor, also asked the central government to hand back control over Catalonia's finances after Madrid said it would maintain its oversight on spending in the region to prevent it from funding a fresh secession bid.
"We won't accept these conditions," Torra said, as Madrid prepares to otherwise lift direct rule it imposed on Catalonia after Puigdemont and other separatist leaders declared independence on October 27th.
Torra, a 55-year-old editor who has long campaigned for independence, was appointed Catalan president on Monday after scraping through a regional parliamentary vote.
He described himself as a "caretaker president" as he awaits the return of Puigdemont, whom he considers the "legitimate" leader.
A series of tweets and articles over past years have overshadowed his appointment, with independent, anti-racism group SOS Racisme Catalunya slamming them on Tuesday.
"We reject the discourse that Mr Torra has used repeatedly," the group said.
"A dangerous, irresponsible and unacceptable discourse, based in prejudices," a statement said, adding it would remain vigilant to denounce any potential "racist stances".
In a series of articles published online, Torra said it was not "natural" to speak Spanish in Catalonia. He also described Spain as "a country that exports misery" and branded those who do not defend the Catalan language and culture "scavengers, vipers and hyenas."
A since-deleted tweet he posted in 2012 said: "The Spanish are coming to monitor us, out of here once and for all!".
Torra has also said a new armed uprising was necessary, just like the one Francesc Macia, Catalan president from 1931 to 1933, planned in 1926 against the military dictatorship of Miguel Primo de Rivera.
"He defends xenophobia," Ines Arrimadas, the leader in Catalonia of the centre-right, anti-independence Ciudadanos party, said Monday.
Foreign Minister Alfonso Dastis added Tuesday he was concerned over a "discriminatory form of nationalism" in Catalonia, according to a statement by a forum in which he took part in the southern city of Sevilla.
The allegations could harm the separatist movement in Catalonia which has always strived to differentiate itself from radical, xenophobic nationalisms that have arisen elsewhere in Europe.
It is estimated that more than 60 percent of the region's 7.5 million inhabitants originate from other parts of Spain.
While the pro-independence movement has grown in strength over the years, the region remains deeply divided on the issue.
Torra has repeatedly apologised for his past comments, which he said were taken out of context.
Responding to the controversy from Berlin, he quoted Macia, whom he said offered to the rest of Spanish people the fraternity of the people of Catalonia when he proclaimed a Catalan republic in 1931.
It is "with the same aim that I am taking the presidency of Catalonia, fraternity to all the peoples of Spain," he said in English.
Jailed, exiled ministers back?
Torra also said that all regional ministers sacked by Madrid after the failed secession bid -- many of whom are now jailed or exiled and face rebellion charges -- will be allowed to return to their posts in his government if they want to.
But this could throw a spanner in the works.
"If this option was put on the table, we would have to look into it and determine if it is in line with the law and justifies lifting" direct rule, Spain's central government representative in Catalonia, Enric Millo, warned on Catalan television.
By AFP's Damien Stroka with Daniel Bosque in Barcelona