"Prime Minister (Narendra) Modi asked the President to visit India and wanted the visit to take place this month itself. But, he (Sirisena) said this month may not be possible because he is still settling down, but early next month is OK," government spokesman Rajitha Senaratne told reporters in Colombo on Saturday.
Modi, during his telephonic talk to congratulate Sirisena, had invited him to Delhi at his earliest convenience, Senaratne said.
As a goodwill gesture, Sirisena decided to free all Indian fishermen in Sri Lankan custody and would take a decision on the fate of Indian trawlers that have been seized by local authorities, he said.
Sirisena, in his address to the nation soon after being sworn-in on Friday, said he would work to mend Sri Lanka's relations with neighbouring nations as well as the international community and overseas institutions.
"We will work with friendship and brotherhood and cooperation with all states," he had said.
Meanwhile, the 63-year-old Lankan leader today began assembling a "national unity" cabinet and invited exiled dissidents back to the country.
A day after his stunning victory deposing the formidable Mahinda Rajapaksa in the presidential election, the new President is planning to include ministers from a cross-section of parties.
He also began a purge of the bureaucracy of the Rajapaksa regime, appointing Rajitha Senaratne as the government spokesman. P B Abeykoon, a senior civil servant, has replaced Lalith Weeratunga as the Presidential Secretary or the head of the civil service.
"The President will name some ministers next week and the balance after the Pope's visit," from January 13 to 15, Senaratne, who is tipped to become health minister, said.
Sirisena, who had promised a 100-day programme to carry out urgent political and economic reforms, has ordered the immediate lifting of censorship on dissident websites, an end to phone tapping, surveillance of journalists and politicians, and the establishment of a right to information law.
Sri Lankan journalists and other dissidents, who had fled the country, were invited back on the promise that criticism was welcome.
Sirisena himself made no public comments today and he is expected to make an address in the hill town of Kandy tomorrow.
On Friday shortly after being sworn-in, the new President had appointed as his Prime Minister opposition leader in Parliament Ranil Wickeramasinghe who is said to have good relations with the West and India.
Senaratne said Prime Minister Narendra Modi and British Premier David Cameron were among the first to congratulate Sirisena.
Senaratne also alleged that Rajapaksa tried to persuade the army chief to deploy troops when it became clear he had lost the polls.
"The army chief was under pressure to deploy but he did not. He declined to do anything illegal," Senaratne said.
"Even in the last hour, he (Rajapaksa) tried to remain in office. Only when he realised that he had no other option, he decided to go," he said.
Rajapaksa has been widely praised for conceding defeat early on Friday, even before the last votes had been counted, when his rival Sirisena had gained an unassailable lead.
"We appreciate the straightforwardness of the Army Commander, Inspector General of Police and the Commissioner of Elections," Senaratne said.
"They stood to uphold the democratic traditions for free and fair election," he said.
In the run-up to the election, then opposition leaders had charged that the military was to be deployed in the former conflict zones in the north to disrupt the polls. The military had denied the accusations then.
A low poll in Tamil areas was seen as favourable to the then President Rajapaksa. The former president, who was seen as being popular among the Sinhala majority for his defeat of the Liberation Tigers of Tamil Eelam, was banking on the majority vote for his re-election.
Sirisena received overwhelming Tamil support as voting was conducted peacefully in the Tamil-dominated regions.
Sirisena's electoral triumph ended Rajapaksa's 10-year-rule and dashed his hopes of winning a record third term in office.
In another significant shake up of the bureaucracy, the powerful Defence Secretary's position was entrusted in the hands of U D Abeykoon. The little known administrator has held the post of Environment Ministry Secretary in the past.
The defense secretary's position was held by Gotabhaya Rajapaksa, the youngest of the three Rajapaksa brothers, in the previous government.
Gotabhaya spearheaded the military campaign which crushed the LTTE in 2009. He wielded a lot of power under his brother's administration.
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