The health ministry blames the rise in infections on the public’s complacency to social distancing and wearing of masks.
Mr Museveni said the country cannot remain under restrictions indefinitely, citing the economy’s weakened health in the wake of the pandemic.
The president said international borders will be reopened for tourists, while returning Ugandan citizens who have tested negative for Covid-19 will be allowed to self-isolate at home.
He said tourists should have taken a Covid-19 test at least 72 hours before arrival and they will be taken straight to their holiday destinations.
Places of worship have been allowed to reopen but the number of congregants will be limited to 70.
Final-year students in primary, secondary and tertiary institutions will resume learning in mid-October, but a decision on the other categories of learners will be made by January next year.
A ban on private and public transport has been lifted in districts bordering neighbouring countries.
Outdoor sports activities have been allowed to resume but with no spectators. Participating teams will be quarantined for the season, with players tested 72 hours before games and after every 14 days.
A ban on public gathering and a night-time curfew still remain in force.
The country began easing restrictions in May but rate of infection continues to rise. Some 6,000 coronavirus cases have so far been confirmed with 63 deaths.
The country’s central bank governor warned in June that further restrictions would disrupt the economy. The tourism sector that earned the country about $1.4bn (£1.08bn) in 2017 is among the worst-hit.