William B. Taylor was U.S. ambassador to Ukraine from 2006 to 2009 and is vice president for the Middle East and Africa at the United States Institute of Peace. Steven K. Pifer was U.S. ambassador to Ukraine from 1998 to 2000 and is a senior fellow at the Brookings Institution. John E. Herbst was U.S. ambassador to Ukraine from 2003 to 2006 and directs the Center for Complex Operations at National Defense University. They collaborated on this op-ed with the other two former U.S. ambassadors to Ukraine, Roman Popadiuk and William Green Miller.

The Ukrainians will fight. For the past few days, the Russian military has attempted to provoke the Ukrainians into making the mistake the Georgians made in 2008: shooting first. First, Russia sent unmarked troops off their base in Sevastopol; the Ukrainians did not take the bait. Next, the Russians sent armored units up the road to Simferopol, the capital of Crimea, but still the Ukrainians did not respond with violence. Then these unmarked troops took over airfields and administration buildings around Crimea, effectively occupying the peninsula. The Ukrainians put their military forces on high alert and called up their military reserves — but have not attacked. This restraint is wise but agonizing. If the Russians attack Ukrainian forces in Crimea or eastern Ukraine, the Ukrainian military will respond, and the war would be terrible.

Neither the Russian nor the Ukrainian military is a formidable fighting force. Economic pressures have starved both militaries of resources; readiness is low, and morale in general is not high. But a Russian attack on Ukrainian forces or a Russian invasion of eastern Ukraine would change some of that. Ukrainian forces from all over the country would converge to fiercely resist the invasion.

When we each served as U.S. ambassador in Ukraine, we visited Ukrainian military bases, talked to commanders and troops, observed training and evaluated units. Many of these units are well-equipped with operational tanks, artillery and transport. One of us jumped with an elite airborne unit whose combat readiness and morale, in contrast to other units, were high. A Russian attack on Ukrainian forces or territory would result in classic and bloody tank warfare the likes of which Europe has not seen since World War II.

It doesn’t have to be.

Vladi­mir Putin is not insane. The condemnations considered so far — cancelling the Group of Eight meeting to be held in Sochi; expelling Russia from the G-8; personal financial sanctions and travel bans on Russian officials whose actions violate international law; meetings of NATO, the U.N. Security Council and European foreign ministers at which Russia is excoriated; and even broad economic sanctions, as were placed on South Africa and Iran — may influence his decisions on next steps. He clearly had wanted to bring Russia back to the big table, an effort that is being destroyed in front of him. An invasion of Ukraine brands him an international outlaw. So he may reconsider.

The Ukrainians should leave an opening for Putin to back down.

First, they should continue to exercise restraint in the face of Russian aggression: Don’t shoot first.

Second, they should continue to make clear that there is no threat to Russian citizens and Russian speakers in Ukraine and that the new government in Kiev intends to represent and serve all Ukrainians. Interim President Oleksandr Turchynov’s veto of legislation that would have demoted the Russian language is one concrete action to highlight.

Third, they should invite international monitors to patrol Ukraine’s eastern border, report on any hostile actions and reassure the international community that minorities, including Russians, are being treated fairly.

Fourth, the new government in Kiev should bring in moderate politicians from the east, including members of the Party of Regions who have disowned Viktor Yanukovych, the president who fled last week.

Fifth, the new government in Kiev should be willing to sit down with Putin in the presence of international mediators and discuss a return to the status quo ante or a mutually agreeable compromise, possibly based on enhanced autonomy for Crimea within a united Ukraine.

Others can help. Ukraine needs financial support from the International Monetary Fund, the United States and Europe. It also needs to know that it has a place in Europe. Beyond the association agreement with the European Union that should now be signed, Ukrainians will want to know that if they undertake the painful economic and political reforms required, membership in the E.U. is a possibility, even if a distant prospect. NATO can play a role by recognizing the threat a rogue Russia poses to member states, especially the Baltics.

Ukraine has suffered at the hands of Russian and Soviet leaders for centuries — memories of Joseph Stalin’s genocide by starvation in the 1930s are still raw. It wouldn’t take much to spark violence and, as Prime Minister Arseniy Yatseniuk has said, war. It can happen; and if it does,Ukrainians will fight. Ukraine, Russia, Europe and the United States should do all in their respective powers to avoid war.