Pheu Thai Party representative Sukhumpong Ngonkham, Move Forward secretary-general Chaitawat Tulathon, Prachachat secretary-general Tawee Sodsong and Thai Liberal Party strategic committee chairman Somchai Srisutthiyakorn issued the plea.
Somchai said votes from 1.3 million Thai voters living abroad are important, expecting around 1 million Thais to be voting.
"About 100,000 voters cast their ballots during the general election in 2019," he said, adding that the number could rise further if the EC and Foreign Ministry facilitate them.
He said that Thai voters living abroad can cast ballots at Thai embassies, mobile polling stations and by post.
"Most voters cast ballots by post," he said, adding that a few voters cast ballots at embassies due to inconvenience in travelling.
He claimed that Thai voters faced difficulties in many countries, such as Malaysia, Singapore, the Philippines, Jordan, Egypt, Belgium and the Netherlands, due to their move to suspend casting of ballots by post.
Thai voters also faced difficulties from many countries' move to schedule the ballot casting period on working days, he said. He explained that Belgium allowed voters to cast ballots on a Tuesday, while Malaysia allowed them to do so on Thursday or Friday.
He added that Thailand did not give voters living abroad enough time to exercise their right. For instance, the ballots would be delivered to Thai embassies on April 22, but the embassies would tell voters to send their ballots by post on April 28, he said.
"Hence, the EC must join hands with Foreign Ministry in asking Thai embassies to give priority to receiving ballots by post," he said.
He also asked embassies to schedule the ballot casting days on holidays and extend the ballot submission period. In addition, vote counting can be conducted at embassies in line with laws, he added.
Echoing Somchai, Prachachat's Tawee said Thai voters living abroad faced difficulties in casting their ballots at embassies. "Votes from Thai voters living abroad can change Thai politics," he said.
Move Forward's Chaitawat said voters had placed high hopes on the upcoming general election.
"Voters were also uncertain whether the election would be held fairly," he said, adding that most Thai voters living abroad cast ballots for democratic political parties.
He urged the EC to be transparent in holding the general election this year.
Pheu Thai's Sukhumpong said the EC could improve the election process by following their advice immediately, so that more Thais living abroad could vote in the May 14 election.