"Our peoples and economies are still suffering from this shock. However, we will do our best to overcome this crisis through worldwide cooperation", he said, as de facto leader Crown Prince Mohammed bin Salman looked on.
He said the G20 represented 90 per cent of the global economy.
He said Turkey is in favour of fair share of global growth within the World Trade Organisation (WTO) rules but demanded a reform process of WTO.
"We have a duty to rise to the challenge together during this summit and give a strong message of hope and reassurance to our people by adopting policies to mitigate this crisis", he told world leaders in opening remarks.
The European Union wants the G20 to invest $4.5bn (€3.7 billion) to help, as well as agreeing new global standards for tackling pandemics.
"We must first put the disease under control at home and, on that basis, strengthen exchanges and cooperation to help countries in need", he said.
China, where the pandemic originated a year ago, also offered to cooperate on vaccines. China has five home-grown candidates undergoing Phase III trials.
China is positive to the global cooperation of developing COVID-19 vaccines. The country has joined the COVAX and wishes to work with other countries in the research, production, and distribution of COVID-19 vaccines.
With Saudi hopes for a grand coming-out parade dashed due to the pandemic, the event has been reduced to brief online sessions of what observers call "digital diplomacy".
The phone call came on the eve of the G20 leaders' summit hosted by Riyadh on Saturday and Sunday. The G20 should respect the World Health Organization (WHO) and create a global mechanism coping with pandemics.
"We will spare no effort to ensure their affordable and equitable access for all people, consistent with members' commitments to incentivise innovation", the leaders said in a draft G20 communique seen by Reuters.
"President Erdogan and King Salman agreed on keeping channels of dialogue open in order for the bilateral relations to be enhanced and for issues to be settled", the presidency said.
Discussions are expected to be dominated by the pandemic's implications and steps for reviving the global economy.
But G20 leaders face mounting pressure to help stave off possible credit defaults across developing nations.
Last week, the bloc's finance ministers declared a "common framework" for an extended debt restructuring plan for virus-ravaged countries, but campaigners say the measure is insufficient. President-elect Joe Biden has not said whether he will join it.
European members of the G-20 are likely to push for more.
But some Western officials have indicated human rights will not be raised at the summit, saying they prefer to use bilateral forums to discuss the issue with the Saudi government. "For humanity to prosper, every single individual must prosper", he said.
The communique offered no details on how the effort will be funded.