Talking to media persons through video conference, Narayanasamy said the chief ministers pointed out that states do not have sufficient funds because economic activity was at a virtual standstill.
He said they raised issues concerning unorgsed labour, agriculture labour, construction and migrant labours, small shop owners and MSMEs.
He said the states demanded a moratorium on dues to be paid to the Centre and extension of the limit under the FRBM Act.
They also sought full-proof mechsm for supply of essential commodities.
Narayanasamy said West Bengal Chief Minister Mamta Banerjee complained that when the country was facing COVID-19, some governors and Lieutenant Governors were "playing politics".
The Congress leader said she told the Prime Minister that they should not "interfere" in the day-to-day administration.
The chief ministers also sought a moratorium on loans by industries and package for them.
He said Puducherry has not received money from the Centre during the lockdown but they had taken a series of welfare measures for vulnerable sections.
"The GST compensation has not come for the last four months," he said, adding that the union territory was facing problems due to insufficient revenue.
Naryanasamy said Telangana Chief Minister pointed out that revenue of state had come to one-tenth of the earlier figure.
The Congress leader said that Modi told the meeting that farm activity should continue.
He said the Prime Minister also said that hospitals should treat not only for the coronavirus affected people but also other normal patients who are suffering.
Narayansamy said the central government will give guidelines to the states to start various activities in a graded manner and there was a suggestion to divide construction industry into green, orange and red zones.
( With inputs from ANI )