Trump is expected to visit Israel and the occupied Palestinian territories on May 22 and 23.
The official Wafa news agency reported that Abbas pointed out that such recognition must be based on the right of return, the right to self-determination and the establishment of an independent state based on the pre-1967 borders, with East Jerusalem as its capital.
On his part, Abbas expressed his appreciation for India's continued support and solidarity for the Palestinian cause on worldwide forums.
US officials planning the trip reportedly rejected an offer by Israeli Prime Minister Benjamin Netanyahu to accompany Trump, saying Monday that the Western Wall was in the West Bank.
New Delhi is hosting Abbas ahead of Hindu nationalist Modi's unprecedented visit to Israel reportedly in July - the first-ever by an Indian premier - with observers calling it a balancing act by India to assuage both sides.
He said that Palestine was ready to make peace and hoped for a response from Israeli Prime Minister Benjamin Netanyahu.
Modi's remarks come ahead of his scheduled visit to the Jewish state and assume significance in the backdrop of growing proximity between India and Israel.
Pippa Middleton Wedding Dress - Taken In Five Times
Word got out last week that Prince Harry's girlfriend, Meghan Markle would be in attendance as the Prince's date. "Pippa's view is that it wouldn't be appropriate for her to be there after a few months of dating".
Prime Minister Narendra Modi has urged Israel and Palestine to find comprehensive resolution to the long-standing territorial dispute between them even as he vowed India's help in the reconstruction and development of Palestine.
President Abbas said India is their "dost" (friend) and briefed Modi about his meetings with US President Donald Trump, Russian President Vladimir Putting and the German leadership.
He has also advocated breaking with decades of precedent by moving the American embassy from Tel Aviv to the disputed city of Jerusalem, a prospect deeply alarming to Palestinians. "We condemn all their barbaric activities", he said.
The Media Committee of the Commission of Detainees and Ex-Detainees Affairs and the Palestinian Prisoners' society, present the summary of the twenty-ninth day of the collective hunger strike, which was embarked by the prisoners' movement in the Israeli jails, under the title of "Freedom and Dignity strike" since 17th April, 2017.
Trump drew global criticism in February when, during a news conference with Netanyahu, he appeared to back away from a US commitment to Palestinian statehood, saying he would leave it up to the parties to decide. This is his fifth visit to India and the third state visit after his visits in 2008 and 2012.
South Africa's Trade and Industry Minister Rob Davies completed the symbolic hunger strike saying, " This is a very small gesture of solidarity with those courageous freedom fighters of Palestine struggling for the very same rights many of us now take for granted in South Africa, but which were in fact won through the same spirit of selfless commitment".