The opposition People's Party (PP) is urging the government to withdraw the charges against American academic Paul Chambers for the sake of the tariff talks with the United States.
Former PM Thaksin Shinawatra has linked the postponed talks on tariffs to US concerns about national security.
He has also noted Thai cases against "some Americans", which could be a reference to the lese-majeste and computer crime charges against Mr Chambers.
Mr Chambers, a lecturer and special adviser on international affairs at Naresuan University in Phitsanulok, was charged this month.
"I thank Mr Thaksin for speaking on the issue, but it is a shame that he is not part of the government or the negotiation team, so I'm not sure how his comment will lead to a solution," said Sirikanya Tansakun, an MP and deputy leader of the PP, adding the government should verify Mr Thaksin's claims for the public.
She said dropping the charges against Mr Chambers may help get the US tariffs talks moving. Ms Sirikanya also criticised the government's lack of response despite repeated warnings during previous censure debates and tariff discussions, stressing it has played the wrong cards.
She urged the media to press the government for a clear answer on the truth behind Thaksin's remarks.
Asked whether Thaksin's reported ties to figures close to US President Donald Trump could help get the talks moving, Ms Sirikanya said all channels should be used, but formal government-to-government negotiations would remain the most effective route.
The MP also acknowledged the Uyghur deportation issue might be an obstacle to the Thailand-US tariff talks, saying this is a sensitive matter which might affect Thailand's relations with China.
