Red Bull had the device on their car at the start of testing at Silverstone, becoming the second team to try it out after Ferrari, but team principal Christian Horner said he was not a fan of the "inelegant solution".
"I'd prefer there to be more research time taken to do the job properly, rather than rushing something through that may have other consequences," he told reporters after Sunday's British Grand Prix.
"I certainly wouldn't vote in favour at the moment."
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Force India deputy principal Bob Fernley told Sky Sports television on Tuesday, with rain teeming down at Silverstone, that he agreed with Horner.
"I believe that it's too hasty. We need to do a lot more work to understand that the halo isn't going to create other problems, which I think it will do," he said.
"I think we should take our time and get the right solution and then introduce it."
The concept, more like a wishbone with a central pillar supporting a protective loop above the driver's head, has been promoted by Ferrari and Mercedes, whereas Red Bull prefer their own 'aeroscreen'.
The latter device, more attractive to some, did not perform as well in testing by the governing body and the halo is now the main focus.
The International Automobile Federation (FIA) is keen to introduce it next year but that would require a unanimous vote by top teams, including Red Bull, as a change to the technical regulations.
The FIA could impose it on safety grounds, however, while approval for 2018 would require only a majority vote.
Ferrari tested a second version of the halo last Friday in British Grand Prix practice but four times world champion Sebastian Vettel, who did a lap with it, said visibility remained a concern.
The device was modified from an earlier version, removing some weight and reducing the risk of the driver's head striking it in the event of an impact.
Improving head protection has become a priority after the deaths last year of Briton Justin Wilson, hit by debris in an IndyCar crash, and Frenchman Jules Bianchi, who suffered ultimately fatal injuries at the 2014 Japanese Grand Prix.
The halo aims to protect the driver's head and deflect large debris and objects, such as bouncing wheels.
(Editing by Amlan Chakraborty/Rex Gowar)
