Calls for the council to stop investing in fossil fuels through its pension fund have been rejected.
Labour councillors called on Medway to suspend investment through the Kent Pension Fund in non-renewable energy sources.
The website Divest.org – which campaigns for local authorities to cease investment funds, stocks or bonds with companies it feels are "unethical" – claims £210 million of the £5.7 billion pot is invested in fossil fuels.
The motion presented at Thursday's full council meeting was supported by the Greens and Lib Dems.
While Labour argued the move would demonstrate the authority's dedication to helping the environment and was in line with their climate change action plan, many Tories were of the opinion this would amount to abandoning fossil fuels altogether.
Cllr Adrian Gulvin (Con) said the scheme invests in banks, a money market fund, and properties, but does not directly invest in fossil fuels.
He explained the fund is administered by Kent County Council and includes around 500 companies and 120,000 members.
He went on to call for more investment in fracking due to the reliance the UK currently has on Russian energy and the conflict in Ukraine.
Cllr Stuart Tranter (Con) added the council wants to move towards greener options, but accused Labour of virtue signalling through their motion.
He said: "These huge funds have legal obligations to deliver pension funds today, and cannot be overturned on a sixpence towards utopian ideals regardless of any well-meaning intentions."
Deputy Labour leader Cllr Teresa Murray said the motion would show the council is prepared to take action against fossil fuel companies.
Cllr Harinder Mahil (Lab) accused opposite members of missing the point, saying: "Sound investment over time is not going to bankrupt or absolutely kill off fossil fuel companies."
He added divestment was "a way we can look more ethically at our approach to investment".
The motion was lost despite winning support from all Labour members and the council's two Independents.