Prime Minister Modi conveyed his good wishes for the progress and prosperity of the friendly people of Malaysia.
Najib said earlier on Facebook he accepted responsibility for the election loss, and while on holiday would consider his position as president of the United Malay National Organisation (UMNO) party and chairman of the routed Barisan Nasional coalition.
After his flight schedule was made public on Friday night, Najib tweeted that he was taking a "short break" to spend time with his family and apologised for his "shortcomings and mistakes".
"We will watch the market and take necessary action whichever way the market goes", Prime Minister Mahathir Mohamad said on Saturday, after offshore investors expressed concern that his populist promises could undermine economic prospects.
Malaysia's new finance minister is seen as a safe pair of hands as he takes on the huge task of bringing down debt while scrapping a consumption tax that was key to Prime Minister Mahathir Mohamad's unexpected election win last week.
"We accept the people's verdict with an open heart", Najib said.
Dr Mahathir has said he is lifting any restrictions from the Official Secrets Act on publicising the details of a report into 1MDB, the state fund started by Mr Najib in 2009.
Some of that money is alleged to have ended up in Najib's personal bank account.
Man City record will be tough to break-Guardiola
And defender Angel Rangel, who is to depart, called on the Swansea board to ensure the club return swiftly to the top flight. Swansea and Stoke, two sides who conceded 124 goals between them this season, could only wish for such solidity at the back.
These funds control billions of dollars in assets, including significant shareholdings in some of the country's biggest publicly traded companies, including banks.
During his election campaign, Mr Mahathir had said that if his Pakatan Harapan coalition won power they would "abolish or cancel" the laws, along with several others deemed "oppressive". There was no sign that Najib or Rosmah had come to the airport. Mr Mahathir sacked Mr Anwar from his post as deputy prime minister and jailed him on a dubious sodomy charge in 1999.
Mr Najib was banned from leaving the country on Saturday after he said he would take a short break overseas to consider his future.
Mahathir has been prime minister of the Muslim Malay-majority nation earlier, for 22 years, governing in a tough, direct style.
New Malaysian Prime Minister Mahathir Mohamad vowed Sunday to review a controversial law against "fake news" hurriedly passed before the elections and seen as aimed at critics of his scandal-tainted predecessor.
"I don't consider myself as a Chinese, I am a Malaysian".
Anwar's daughter and a member of Parliament, said that the board was expected to rule that there had been a miscarriage of justice and that her father was innocent.