In a letter to Xi, Modi expressed solidarity with the president and people of China over the outbreak of the virus, official sources said.
A total of 811 people have died of the coronavirus infection in China so far while the number of confirmed cases has gone up to 37,198, according to latest data released by Chinese authorities.
Though the epicentre of the outbreak was Hubei province, the virus has spread to almost every province in China as well as around 25 countries in the world, forcing the World Health Organization to declare it a global emergency.
In the letter to Xi, Modi offered India's assistance to China to deal with the challenge and also conveyed condolences at the unfortunate loss of lives due to the outbreak, the sources said.
The prime minister also conveyed to Xi his appreciation for facilitating evacuation of around 650 Indian citizens from the Hubei province last week.
A sizeable number of countries have evacuated their citizens from China and restricted movement of people and goods to and from China.
India too has put restrictions on the movement of people to and from China as part of precautionary measures to contain the spread of the virus.
In an interview to PTI, Chinese Ambassador Sun Weidong on Wednesday said China is ready to work with India to strengthen communication and coordination, and to safeguard the health and safety of Indian citizens in China.
Admitting that there could be a short-term impact of the epidemic on China's economy, he said the country's internal resilience is growing and it has ample resources and policy tools to cope with the economic volatility resulting from the outbreak.