Kalam extended the invitation to Singh after a 15-minute meeting with him and Congress president Sonia Gandhi at the Rashtrapati Bhavan.
Emerging from the meeting, Singh told reporters that they made available to the President documents with regard to the support extended by various political parties.
Standing by his side, Sonia Gandhi said, "I think the country will be safe under Dr Manmohan Singh."
Singh said the mandate was for Sonia Gandhi who, in turn, said that now the final decision has been taken and that she was relaxed.
"I was under tremendous pressure but now everything is over... it is a happy moment," she said.
When asked whether he was a reluctant Prime Minister, Singh said, "The mandate of the people of India was to Sonia Gandhi as Prime Minister."
"We all persuaded her to accept the verdict of the people but she declined due to reasons spelt out by her in her statement," he said.
In his message to the market, Singh said his Government recognised the importance of healthy capital market and there was no reason for anyone to panic.
"Our Government recognises the importance of healthy capital market," Singh said.
Policies of the new Government will include responsible macro-economic policies, bringing balance in growth and focus on agriculture, viable social safety net and creation of job opportunities.
"We have always said that economic reforms with human face will continue," he said.
Singh also said 21st century will be India's century.
