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Negotiators from both countries have struggled for more than a year to conclude a trade package as New Delhi and Washington spar over a range of issues, including tariffs.
Prime Minister Modi, who is visiting the US for the 7th time after assuming office in 2014, described Friday's bilateral summit with Biden as important as they're meeting at the start of the third decade of this century.
Garcetti, a Biden loyalist who co-chaired the successful Biden-Harris 2020 election campaign, has served as mayor of Los Angeles since 2013.
The US on Sunday finally agreed to provide it raw materials for vaccines that had previously been under export controls, as well as other key material.
Biden is known to be a strong proponent of closer India-US ties since his days as a senator in the 1970s and played a key role in getting the approval of the Senate for the bilateral civil nuclear deal in 2008.
Though the ties between the two democracies will continue to grow, there is a definite possibility of a change in nuance in handling key issues by Biden as he is expected to be less unilateralist on trade and more moderate on immigration and visas, experts said.
Addressing the US-India Strategic Partnership Forum through video conference, Modi also cited a slew of reforms undertaken by his government and asserted that India is committed to democracy and diversity and it has undertaken far-reaching reforms in recent months.
Both India and China have expressed their desires to de-escalate and the US supports a peaceful resolution of the current situation, the spokesperson said.
The White House said the US president and Indian Prime Minister Narendra Modi are working towards a trade pact that reflects the full potential of the economic partnership between both nation.
Trump's daughter Ivanka, son-in-law Jared Kushner and several top officials of the US administration were also present at the ceremony.