Volodymyr Zelenskyy has said that stabilisation measures are under way and have been completed in towns and villages across a 4,000 sq km area.
In his daily Telegram post, the Ukrainian president said stabilisation is continuing in other areas his forces have taken in the last week or so.
On Tuesday, Ukraine’s military pushed into the town of Vovchansk, about 3km (2 miles) from the Russian border, about 60km (37 miles) northeast of Kharkiv.
He also pledged to look after pensioners and to make sure life returns to normal as quickly as possible.
Mr Zelenskyy said: “As of now, stabilization measures have been completed in the districts with a total area of more than 4,000 square kilometers. Stabilization continues in the liberated territory of approximately the same size.
“Remnants of occupiers and sabotage groups are being detected, collaborators are being detained and full security is being restored.
“It is very important that together with our troops, with our flag, ordinary normal life comes to the de-occupied territory.
“As an example, in Balakliia, in Hrakove, the payment of pensions for five months at once, for the time when we simply could not make payments due to the occupation, has already been started.
“And all Ukrainian pensioners in the liberated territory will receive payments. Ukraine always fulfills its social obligations to people.”
Earlier, he said Ukraine had recaptured around 8,000 sq km (3,100 sq miles), apparently all in the northeastern region of Kharkiv.
That was 2,000 sq km more than he said Ukraine had recaptured on Monday.
