The phrase 'continuing towards' is correct and usable in written English.
You can use it to convey the idea that an action is proceeding toward a destination, and there is no sign that it will stop. For example: "The runners continued towards the finish line, determined to be the first across."
Arikha drew Beckett constantly, with his beaked bird's profile, in silverpoint, ink and crayon: playing chess, smoking, listening, pushing back his glasses.Beckett's plays, with their theme of constant striving against the odds, their inevitable failure but determined continuing towards some sort of truth, fitted exactly with Arikha's notions of his art.
Continuing towards the west-northwest, the hurricane regained strength as it moved over the northern Caribbean.
After a while, the dense housing becomes farmland and fields, with the highway continuing towards downtown Marcellus.
The highway proceeds north into Caddo Lake State Park, passing around the park headquarters building, and continuing towards cabin sites.
In either case, Suleiman withdrew at the arrival of the August rains, and returned homeward instead of continuing towards Vienna as previously planned.
Continuing towards the northeast, the storm remained weak and was last mentioned as it crossed the international date line on June 14 near the Aleutian Islands.
The decision to continue towards strikes is a risky one from a PR perspective.
The ships did not heed that call and continued towards Gaza.
Whether this progress can continue towards democracy and prosperity depends upon a whole cascade of uncertainties.
As women MPs and ministers continue towards the exit door, the new face of Gordon Brown's government is becoming clear.
There will always be more to do but we expect that progress to continue as we continue towards a truly equal workforce in all sectors".
