The US is providing oxygen-related supplies, vaccine materials and other relief. After a call between Modi and US president Joe Biden, the White House said the two leaders stood "shoulder to shoulder" in the effort to protect people.
Separately, the US said it would share 60m doses of the Oxford/AstraZeneca vaccine with other countries as the jabs become available, although it is unclear how many of these will be sent to India.
India reported more than 354,000 new infections on Monday alone, along with 2,800 deaths. Experts believe the true toll is being vastly undercounted.
France and Germany are part of a broader EU effort to provide assistance to India. Ireland confirmed it would give 700 oxygen concentrators, the European Commission said, after India requested urgent supplies of the vital gas and also antiviral drugs.
The commission has activated the EU's emergency Civil Protection Mechanism at India's request. "We are in close contact with both Paris and Berlin to see how this aid can go through the mechanism," a spokesman said.
Cases have overwhelmed health services and sparked acute shortages of hospital beds and life-saving supplies, such as oxygen. New variants, including the B. 1.617 strain discovered in India, are suspected of stoking the surge.
While the EU, US and UK offer to provide emergency supplies including oxygen, ventilators and raw materials for vaccine production have been welcomed, Modi's government has been criticised for ordering the removal of social media posts critical of its handling of the crisis.
Demand for vaccinations has surged as the crisis has spiralled, and India now faces a shortage of jabs. The pace of vaccination has slowed from as many as 4m jabs a day earlier this month to fewer than 3m.
Biden's administration has been under pressure to release some of its stockpile of AstraZeneca doses that have been manufactured but not yet approved for release. Such a move could be legally tricky since the US has reportedly signed contracts with all vaccine makers that forbid the export of any US-made doses.