Interserve tumbled 15% in the opening minutes of trading, after the Financial Times reported a Cabinet Office team was monitoring the outsourcing group and that ministers were 'very worried'.
But the shares recovered some of those losses after the Cabinet Office issued a statement downplaying its efforts.
'We monitor the financial health of all of our strategic suppliers, including Intersetve,' it said.
'We do not believe that any of our strategic suppliers are in a comparable position to Carillion.'
The shares are currently trading at 118p, down 2.5% on the day.
Liberum analyst Joe Brent issued a note reiterating his 'buy' rating on the shares and 180p target price on the shares.
After Carillion's demise, Interserve is now the cheapest stock in the outsourcing sector, with the shares having fallen 76% in the last two years, and debt of around three times its earnings.
'Interserve clearly has too much debt, but we continue to believe it is different from Carillion given lower window dressing, lower restricted cash, no factoring and a small pension deficit,' he said.
'But there are businesses to sell and we believe that shareholders would support a [capital] raise,' he said.
After Carillion's collapse into liquidation on Monday, suppliers of the failed construction group meanwhile continued to update the market on the likely cost they would bear.
Alternative Investment Market (AIM)-listed recruitment business Gattaca (GATC), whose shares tumbled 9.3% yesterday, said most of the money it was owed by Carillion was insured.
'At this time, we estimated our uninsured balance sheet exposure to be less than £100,000. The impact of Carillion's liquidation on our balance sheet will therefore be minimal,' it said, adding that net income from Carillion stood at around £500,000.
That prompted the shares to recover some of yesterday's losses, rising 6.9% to 262p.
Bilby (BILBI), an AIM-listed gas heating, electrical and building services provider, also sought to reassure investors over its work with Carillion, after its shares slumped 15% yesterday.
Bilby has two contracts with the CarillionAmey joint venture servicing the Ministry of Defence.
It highlighted the joint venture's statement on Monday that Amey would take control of the project 'without adverse effect on the employees of the joint venture or its supply chain'. That sent the shares 12.1% higher to 101.5p.