We are writing on behalf of the millions struggling to survive the pandemic far from home. Some have fled wars, conflict, persecution and human-rights violations. Others are moving to escape socioeconomic hardship or climate-change effects.Far from home, many risk exclusion or neglect, facing barriers to accessing vaccinations, testing, treatment and, sometimes, information.The poorest countries often shoulder the greatest responsibility for supporting displaced people and others on the move. They need reliable, adequate vaccines and other critical supplies to stabilise fragile health systems, and save their citizens, migrants and refugees, and others.The vaccine equity gap between wealthier and low-resource countries demonstrates a disregard for the world’s poorest and most vulnerable. For every 100 people in high-income countries, 133 doses of Covid-19 vaccine have been administered, while in low-income countries, it is four per 100 people.Vaccine inequality costs lives, placing everyone at risk. History and science make it clear: coordinated action with equitable access to public health resources is the only way to face down the Covid-19 scourge. We need a strong, collective push to save lives, ensuring a sustainable global recovery.Vaccines are powerful; they’re not the only tool. We need tests to locate the virus, treatments including dexamethasone and medical oxygen to save lives, and tailored measures to prevent transmission.Leaders of the largest economies have the power and responsibility to help stem the pandemic by expanding access to vaccines and other tools where these are in shortest supply.This weekend’s summit in Rome will call for “courage and ambition” to recover from the pandemic and overcome inequality. We collectively call on G20 leaders, to:(1) Increase vaccine supplies for the poorest. The leading economies must fully fund and implement the Strategic Plan and Budget for the ACT Accelerator, and distribute vaccines, tests and treatments where needed. If we are to recover from the pandemic, we must meet the targets to vaccinate 40% of the world’s population by the year’s end – and 70% by mid-2022.(2) Ensure access to vaccines for all people on the move. We call on every country to ensure everyone on its territory, regardless of status (including refugees, migrants, internally displaced people, asylum seekers, others on the move), has access to Covid-19 vaccines, tests and treatment. They should remove barriers to vaccination for all on their territory – for example, the need for specific documents, geographical barriers, the need in some settings to report to immigration authorities, high fees – and fight vaccine misinformation.(3) Support low- and middle-income countries to combat Covid-19 with all available means. These countries need comprehensive support – financial, political, technical, logistical – to vaccinate quickly and effectively, expand access to tests and treatments, implement tailored public health measures, and build resilient systems for future emergencies.We urge you to take swift action to ease the pandemic’s devastating human toll.Filippo Grandi UN High Commissioner for Refugees António Vitorino Director general, International Organization for Migration Tedros Adhanom Ghebreyesus Director general, World Health Organization Have an opinion on anything you’ve read in the Guardian today? Please email us your letter and it will be considered for publication.