Jill Stein and Ajamu Baraka, the presidential and vice-presidential candidates of the Green Party who on Wednesday had arrest warrants issued against them for participating in a protest against the Dakota Access Pipeline earlier this week, say they are proud of their actions and will now "engage the legal process with dignity and integrity."

The pair joined the ongoing protest against the controversial pipeline, known by the acronym DAPL, in North Dakota on Tuesday where their campaign admits they both spray-painted construction equipment alongside tribal activists and environmental allies.

While Stein painted "I approve this message" on one bulldozer, Baraka wrote the phrase "We need decolonization."

For weeks, the multi-site demonstrations against DAPL have grown and intensified as regional tribes also wage a legal battle to have approval of the project cancelled.

On Wednesday, following through on an earlier threat, Morton County sheriff's department charged both Stein and Baraka with misdemeanor criminal trespass and criminal mischief. A spokesperson for the sheriff's office, Rob Keller, told reporters the warrant was officially filed with the county and if local authorities encountered Stein in the area, "they would arrest her."

In a campaign statement released Wednesday night, Stein showed no inclination should would duck from the charges, but said the real crimes taking place in North Dakota should not be ignored.

"Of course I approve the action of ordinary people standing up to the destruction of our climate and sacred sites," Stein said. "Trump and Clinton support the right of corporations to destroy our planet and communities for their profits. Ajamu and I do not."

In an earlier statement Stein said that she hoped North Dakota authorities, instead of focusing on the resistance by tribal members and other protesters, would instead "press charges against the real vandalism taking place at the Standing Rock Sioux reservation: the bulldozing of sacred burial sites and the unleashing of vicious attack dogs." Her campaign, she added, "supports the courageous Indigenous leaders who are taking a stand to protect future generations from the deadly greed of the fossil fuel industry."

Baraka also stood by his actions, saying, "Our campaign is all about standing up to the rich and powerful who believe in their right to exploit the rest of the planet’s beings and resources for their own profit. The state should be prosecuting the crimes of threatening the water of millions and the attacks on peaceful protestors."

The following video includes remarks Stein made while at the protest site on Tuesday: