Giant sunspots remain visible on our star and could continue to hurl many billions of tonnes of superhot gas in our direction, say solar scientists.
Two big explosions were seen on Sunday
On Sunday, two so-called coronal mass ejections blasted material away from the spots and may yet give Earth's magnetic defences a glancing blow.
The surge of charged particles could affect orbiting satellites, and ground based communication and power systems.
At the very least, strong auroras should be seen at high latitudes.
These Northern and Southern Lights are generated when fast-moving particles (electrons and protons) ejected from the Sun get trapped in the magnetic field around the Earth, and collide with the gases in the upper atmosphere.
Experts on space weather say auroras are possible in the United States, Canada, southern Australia, New Zealand, and much of Europe as well.
The increased solar activity of recent days is being monitored by mission controllers looking after the International Space Station.
The current Expedition 7 crew - Russian cosmonaut Yuri Malenchenko and US space agency (Nasa) astronaut Ed Lu - is due to return to Earth on Tuesday along with Spanish astronaut Pedro Duque.
But flight officials are confident radiation levels will not prevent the planned de-orbit.
"As part of our normal support of International Space Station operations, we continually monitor solar activity levels," said Mike Golightly, manager of the space radiation analysis group at Nasa's Johnson Space Center, Houston.
"To date the recent eruptions, or coronal mass ejections, have not resulted in any additional radiation exposure to the crew, nor is any increase expected from these events," he said.
The source of the current activity is some very large sunspots - darker, cooler areas on the Sun where the solar magnetic field pokes through the solar surface.
Instabilities in these spots can lead to huge explosions of gas and charged particles.
The current groups of sunspots are among the largest seen in years - 10 times larger than the surface of the Earth - and two regions, designated "484" and "486", produced X-class (the most powerful) events on Sunday.
What impact these explosions will have on Earth will depend on how much of their force strikes the planet head on.
Experts say there could be blackouts in some radio frequencies. And while TV and broadcast radio stations are much less affected by such conditions, ground-to-air, ship-to-shore, and amateur radio systems could be quite badly hit.
Some orbiting satellites could be in the firing line, too. The mass of electrons contained in these surges can damage onboard microchips. Operations may need to be temporarily suspended to protect sensitive equipment.
Advice to spacecraft owners will come from space weather forecasters with access to the fleet of probes that have been specially built to monitor solar activity and withstand its effects - probes such as Europe's Cluster spacecraft and the European/US Soho satellite.
These provide real-time information about Sun activity and can give many hours' notice of a change in space weather conditions.