Opposition forces, which claim a majority after several defections from Jeremiah Manele's coalition, are urging the prime minister to recall parliament to test its numbers.
A motion of no confidence is waiting for Mr Manele when he does recall MPs to session in Honiara.
However, with no sitting currently scheduled and Mr Manele not eager to regather MPs, the 28-strong opposition says it is now looking to the judiciary.
"This legal action is about upholding the rule of law," a statement from the opposition bloc read.
The application essentially asks the High Court to order parliament to resume, considering "whether the actions, or inaction, of the relevant authorities fall within the bounds of their lawful powers and responsibilities".
The Matthew Wale-led opposition says its preferred outcome is for Mr Manele to recall parliament on his own accord.
"Parliament is the supreme democratic institution of our country and must be allowed to function without obstruction," the statement continued.
"The continued delay in convening parliament, without clear and justifiable reason, does not serve the national interest."
"Rather, it serves only the interests of a narrow few at the expense of the broader democratic will of the people."
Among its 28 members are ex-prime minister Darcy Gordon Lilo, ex-foreign minister Peter Shanel Agovaka, and influential MPs Fredrick Kologeto, Manasseh Maelanga and Peter Kenilorea.
Opposition MPs continue to post photos of the grouping gathering together, showing their strength in numbers.
"Our resolve is strong. We are the government in waiting," Mr Kenilorea said.
Mr Agovaka - who could emerge as the prime minister should the no-confidence motion pass - said relationships in the coalition had completely broken down.
"When the cabinet becomes toxic, that is a problem. We can't work together," he said, as reported by In-Depth Solomons.
"We can't see eye to eye. If (Mr Manele) walks into the room, I walk out. Or if I walk into the room, he walks out. That is toxic."
Earlier this month, Mr Manele told a press conference there was no pressing reason for parliament to meet, and it would next gather around May or June.
A dozen ministers left the coalition, citing instability and weak leadership, in early March.
Mr Manele appointed new ministers in their place - including Manasseh Sogavare as his deputy - and says governance is continuing as normal.
The 58-year-old has survived two motions of no confidence already in his two-year tenure, though this political crisis looks to be a more serious threat to his prime ministership.
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