BSP supremo Mayawati, a major contender to power in the key battleground state, Congress and the DMK criticised the move, saying it was being made for "electoral benefits".
The land for the proposed museum has been provided by the Uttar Pradesh government.
"Developing tourism in Ayodhya is good but, how come the Narendra Modi government thought of developing the Ramayana Sangrahalay (museum) and the state government of Ramleela theme park just before the Assembly polls," she said in a release in Lucknow.
Congress leader and former Union minister R P N Singh accused the Modi government and BJP of invoking Ram months ahead of the assembly polls due early next year for deriving political mileage out of it.
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The proposed museum revived the demand for construction of Ram temple, with BJP hardliners like Union Minister Uma Bharti and Vinay Katiyar pitching for it.
Katiyar went on to demand tabling of a legislation in the Lok Sabha where the BJP-led NDA has a "massive majority".
"Why only Subramanian Swamy, every devotee of Ram wants the temple to be constructed soon. Until that happens we cannot live in peace. Be it through a bill in Parliament, through dialogue or a court verdict, the government has to find a solution.
Uma Bharti, another stormy petrel of the Ram temple movement, said, "The issue is what we, the agitators, were claiming as the place where Lord Ram was born was indeed that place or not. A three-judge bench (of Allahabad High Court) agreed with our contention.
Mahesh Sharma, however, insisted his visit to Ayodhya had nothing to do with the UP polls, but said he would be visiting the makeshift temple at the Ram Janmabhoomi-Babri Masjid complex.
DMK chief M Karunanidhi also deprecated attempts to rake
up the Ram temple issue ahead of UP assemly polls.
"There are reports that BJP is trying to rake up the Ram janmabhoomi issue to garner Hindu votes in Uttar Pradesh," he said in a statement in Chennai.
Karunanidhi, who had earlier triggered a row with his critical comments about Lord Ram made at the height of the Ramasethu controversy, also criticised the move to set up a Ramayana museum.
Sharma, while insisting that the project had nothing to do with politics, said the museum will be a part of the Ramayana Circuit for which the Centre has sanctioned Rs 225 crore, with Rs 151 crore exclusively for Ayodhya, which is the hub of the circuit.
He said the government has identified three circuits-- Ramayana Circuit, Krishna Circuit and Buddhist Circuit-- to boost religious tourism.
Sharma will also hold a meeting with Ramayana Circuit Advisory Board during the visit. The meeting would discuss routes for connecting Ramayana-related sites in Nepal and Sri Lanka with the proposed museum.
The Union Minister would also deliberate on plans for an International Ramayana Conclave, which would be held either in Ayodhya or Chitrakoot district. The conference is likely to be attended by delegates from about 12 countries, sources said.
He said his Ayodhya visit was planned two months back and had nothing to do with the UP assembly elections, which were "planned five years ago".
When asked if the museum will be inaugurated ahead of the UP polls, Sharma said,"It is a continuous process. It will involve development of ghats, infrastructure etc."
Asked to comment on Katiyar's demand for bringing a bill in Parliament for construction of the temple, he said,"I am an Indian first. I am going there as a trourism Minister. Ram temple is on (BJP's) agaida, but (commenting on Katiyar's demand) is not within my purview as Tourism Minister."
Though the BJP has been insisting that Ram temple will not be an electoral plank in the UP elections to be held early next year, the proposed Ramayana museum and related activities are being seen as an attempt to keep pro-Hindutva elements in good humour.
On Dusshera, Prime Minister Narendra Modi had, in a departure from tradition, participated in the festivities in Lucknow where he started and concluded his speech with chants of "Jai Shri Ram, Jai Jai Shri Ram".