Ukraine's swift entry into Russia's Kursk region caught Moscow by surprise, as Kyiv's forces quickly took control of a swath of the border oblast and put their opponent on the defensive.

The pace of Ukraine's gains has since slowed, but not stopped, as Kyiv's troops have hit bridges, captured Russian conscripts, and forced Moscow to deal with an unanticipated attack now in its third week.

And for Ukrainians, whose lives have been upended by 30 months of all-out war with Russia, the audacious push has buoyed their hopes. Yet this optimism is tempered by concerns about how events could still turn — and not necessarily in Ukraine's favour.

WATCH | Problems for Putin in Kursk: 

Ukrainian push into Russia is 'catastrophic' for Putin's plans, former U.S. ambassador says

Ukrainian push into Russia is 'catastrophic' for Putin's plans, former U.S. ambassador says

"The public sees the operations in Kursk as a much-needed boost — morale is up, there's a sense of hope, and immense pride that we can push Russia back, even in their own territory," Tymofiy Mylovanov, an economist and former Ukraine government minister, said via email, from Kyiv.

"However, there are two main concerns: whether we can hold these gains and the real cost in Ukrainian lives."

A surprise even to Ukrainians

The Kursk offensive came as a surprise even to Ukrainians, as they watched their armed forces undertake the largest attack on Russia since the Second World War.

"I have to emphasize that this operation was kept in complete secret," said Yevheniia Kravchuk, a Ukrainian lawmaker and a member of Ukrainian President Volodymyr Zelenskyy's Servant of the People political party.

Kravchuk said Ukrainians have gradually learned more about the Kursk offensive, which began on Aug. 6, and she believes it has provided an "exceptional boost" to the mood of soldiers and civilians alike.

Andriy Kulykov, a Kyiv-based journalist and chair of Ukraine's Hromadske Radio, says the public reaction in Ukraine has been positive, perhaps partly "as people were starved of reports of military success."

However, Oleksiy Goncharenko, a fellow Ukrainian lawmaker who hails from Odesa, sees a broader range of opinions being expressed.

"Some Ukrainians understand and support this operation, some do not. This is a democracy, so everyone has their own opinion," he told CBC News in an emailed statement.

"But we believe in our Armed Forces," he added, noting that Ukraine's parliament has voted to provide additional support for those fighting in the Kursk region.

Those divided opinions can be found on the streets of Kyiv.

"We don't know to what this will lead to, but we all have our hopes high," Olha Pavlovska, a resident of the capital, told Reuters.

Veteran Yaroslav Mandel, meanwhile, told the news agency that the Kursk offensive amounted to "a show" compared to what soldiers in Eastern Ukraine are dealing with.

Viktor Kovalenko, a fellow Ukrainian combat veteran who lives in the United States, says he found the news from Kursk hard to absorb at first, but he then became "cautiously optimistic" about what was unfolding — though he still has concerns about where things could go.

Wider threats to Ukraine

The pressure that Ukraine has put on Russia in the Kursk region has not diminished the problems it faces along other parts of its border — including in Eastern Ukraine, where Russia has made slow and grinding gains in recent months.

There had also been some suggestion that Russia might be compelled to shift some of its troops from Ukraine's eastern region to deal with the situation in Kursk. This does not appear to have been the case so far.

"The initial expectations that the offensive may distract substantial Russian forces from the frontline in Donetsk oblast do not seem to materialize," Kulykov, the Kyiv-based journalist, said in an email.

However, some key goals of Ukraine's offensive — as spelled out by Kyiv — include establishing a "buffer zone" in Kursk to prevent Russian attacks, and capturing Russian soldiers who can be exchanged for Ukrainian prisoners of war.

Kravchuk, the Ukrainian lawmaker, said the return of Ukrainian PoWs is a politically sensitive issue and one on which she feels pressure from constituents.

"They expect that we can exchange our prisoners of war that are still ... in captivity in Russia," she said.

'Real leverage' for Ukraine?

Ukraine's president has stated it's critical that the country strengthen its position ahead of the fall.

Mylovanov, the former government minister, believes the Kursk action gives Ukraine "real leverage," no matter what Moscow may be saying about it.

"Russia, and particularly Putin, are trying to downplay the significance of Kursk to limit our leverage," said Mylovanov. "They've learned the hard way that they can't push us back quickly."

He noted that a fierce Russian retaliation over Kursk could be a risk, as could a lessening of U.S. support — though he said neither seemed likely at the moment.

With a looming U.S. election, there could be implications for Ukraine in terms of future support from Washington — with one of the main presidential contenders, Donald Trump, having repeatedly claimed he'll settle the conflict.

Kovalenko, who served in Ukraine's military a decade ago, believes Kyiv is trying to do what it can to be ready for eventual negotiations with Russia — and it should decide the timing for that on its own.

"Do not force Ukraine to make a deal now," he said.