Vijayan met Prime Minister Narendra Modi here and discussed various issues related to the state, including rail projects.
Vijayan said he had a very cordial and friendly meeting with the Prime Minister, who also expressed his support for major projects in the state.
The Prime Minister also encouraged the state to take up new projects, he added.
Addressing the media in the national capital, Vijayan said he has asked the Prime Minister to immediately provide pending GST (Goods and Services Tax) compensation dues of Rs 4,524 crore related to the 2020-21 fiscal.
There are financial issues and the state needs a lot of help, the chief minister said as he mentioned about raising the GST dues matter with the Prime Minister.
The demand for an AIIMS (All India Institute of Medical Sciences) in Kerala has been pending for a long time.
''We discussed the demand for AIIMS in Kerala and the Prime Minister was very positive in his response,'' Vijayan said.
According to Vijayan, the Prime Minister also expressed his interest in the possibility of inland waterways.
They also discussed about the proposed Angamaly-Sabari railway line, light metro rail projects at Thiruvananthapuram and Kozhikode, city gas distribution issues and proposed petro chemical complex in Kochi, among other matters.
During the meeting, the chief minister urged Modi to provide more COVID vaccines to the state.
Kerala needs around 60 lakh vaccine doses this month and 25 lakh doses are required for those who are to take the second vaccine dose. Vijayan also said that Kerala is a state that does not waste vaccines and so far, 44 per cent of those above 18 years have received their first dose.
Kerala has been witnessing relatively high number of coronavirus infections in recent weeks.
The issues regarding allowing landing of large aircraft at Kozhikode airport and those related to Kannur airport were also discussed.
Vijayan also held meetings with Union ministers Hardeep Singh Puri and Ashwini Vaishnaw.
Puri is the Minister of Housing and Urban Affairs as well as Minister of Petroleum & Natural Gas. Vaishnaw is in charge of the portfolios of Railways, Communications and Electronics and Information Technology.
This is the first visit by Vijayan to the national capital since CPI(M)-led Left Democratic Front (LDF) came back to power in Assembly polls held in April. He took oath as the chief minister for the second time along with 20 ministers on May 20.
To a query regarding traders' demand for opening shops in Kozhikode and that they might not wait for the state government for a decision, Vijayan said the matter will be dealt with accordingly if they resort to a different way.
The comments also come against the backdrop of high number of COVID cases and restrictions in place in different parts of the state to curb spreading of infections.
Puri told the chief minister that permission for the second phase of Kochi Metro would be given immediately, according to an official release. The second phase for 11.2 kilometre-stretch.
Vijayan also said that Kerala has an ''industry friendly'' atmosphere and that entities are exploring big investment opportunities, amid Kitex Group deciding to shelve its investment plan for the state.
In the evening, the chief minister held a meeting with various officials, including Civil Aviation Secretary Pradeep Singh Kharola and Air India CMD Rajiv Bansal.