As directed by the All India Congress Committee (AICC), a Congress delegation led by state president Ashok Choudhary met the Governor and submitted the letter.
"We have handed over letter of support to the JD(U) government," Choudhary told PTI.
With the support of the four-member Congress, the numbers for the new JD(U) government has increased to 124 in the Assembly whose effective strength at present is 239.
Asked about the chances of Congress joining the new ministry to be led by Jitan Ram Manjhi, he said there was no instruction from the Congress leadership.
State Congress Vice President and media in-charge Prem Chand Mishra said Congress support to a secular government in Bihar was "unconditional."
Congress Legislature party leader Sadanand Singh said, "We are continuing our support to JD(U) after it severed ties with BJP."
Congress has four members in the Assembly at present and three members including PCC chief Ashok Choudhary in the Legislature Council.
With Nitish Kumar turning down the plea to withdraw his resignation as Chief Minister and choosing Manjhi as his successor yesterday, a JD(U) delegation had handed over a letter of support of 117 JD(U) MLAs, 2 Independents and 1 CPI to the Governor while staking claim to form the government.
Congress had bailed out JD(U) ministry in Bihar after Nitish Kumar had broken up with BJP in June last year.